Most flights arrive at Ataturk Airport which is on the European side of Istanbul and with good links to the city , Easy Jet fly to Sabiha Gokcen which is a brand new very under used airport on the Asian side and between 45 mins to an hour from Istanbul depending on the traffic.
There is currently a Havas bus service which meets the flights leaving about an hour after you land and going straight to Taksim Square one of the main transport hubs.
You can also get the local E3 Bus to 4 Levent Metro, the metro then goes to Taksim and on to Sishane (Beyoglu) this is simple on the way in and the buses run to time but on the way back finding where the bus starts from is more difficult, ask at the Metro to make sure you use the correct exit.
There are various Airport Transfer Services, check on line for Sabiha Gokcen Airport and there are a couple of useful sites.
The other thing you need to know if you have not been to Turkey before is that you need to buy a Turkish Visa when you land before you go through Passport Control which cost £10 per person.
One of the most valuable pieces of information is about travelling around Istanbul, there are funiculars, trams (old and new), buses, metro and best of all ferries and you can travel on all of them easily if you buy an AKBIL which looks a bit like a key ring and on which, after paying your initial 6 Turkish Lira - £ 2.40 (Refundable), you can then top up with what ever amount you want and you use on the machines that are at all transport stops this gives you discounted travel and makes life very simple.
The Time Out Guide to Istanbul is excellent on getting around, places to see and great eating and drinking choices.
Istanbul is really divided into three parts, the two European sections Sultanahmet which contains the main sites, Beyoglu the other European section which has shopping, and the best selection of eating and drinking places and therefore I think the best area to stay. The third section is the Asian shore which should definitely be visited.
Hotel Galata Antique, Mesrutiyet Caddesi 119, is a lovely old fashioned hotel in Beyoglu just at the top of the Tunel funicular which brings you up from the Galata Bridge linking the two European shores. It is also adjacent to the Sishane Metro stop
There are good discounts depending on the time of year, and further discounts if you pay cash, the rooms are very well appointed, the staff helpful and the price includes breakfast €€
Other hotels in the Beyoglu area are available on various web sites, although some of the bigger ones nearer Taksim Square are probably a bit far for you to enjoy properly the various districts making up Beyoglu
There are now lots of apartments available and there are some lovely ones around Beyoglu.
Mozaik (formerly Rumeli) (Sultanahmet) Corner of Incil Cavus Sokaka & Ticarethane Sokak 8, off Divanyolu Caddesi (Tram Route) this restaurant is near the Blue Mosque and is in a lovely street just off the main drag it does a modern twist on traditional Turkish dishes as well as excellent salads, very good service €€
New Galata on the lower deck of the Galata Bridge there are dozens of places to eat on the bridge all of which will try and drag you in. This was the only one we tried and the fish, which all these places specialise in was good, watch as they try and talk you up in what you have but the views can’t be beaten €€
On the Beyoglu side of the Galata Bridge on the left facing Sultanahment near the main Karakoy Ferry stop is a fish restaurant called Olympiat which although they can be pushy is very reasonably priced if you stick to your guns and have the fish like bream and bass priced as a whole fish and not by weight - also the views are great.
At the Beyoglu end of the bridge on the left as you cross are loads of fish stall and little places with just a grill and a few tables where you can eat very basically and very cheaply € There are smarter ones on the Sultanahment side where fish in a roll is 4 Turkish Lira - you go up to the boat and order then grab your seat, they come round with soft drinks and pickels and also wet wipes (very handy).
Krependeki Imroz (Beyoglu) Nevizade Sokak 16, is one in a narrow street lined with places but this is reckoned to be one of the best “Meyhanes” (traditional Turkish eating places) in Istanbul great meze starters then grilled fish or meat €- €€ There are another couple in the same street also recommended in the Time Out Guide.
Sofyali 9, (Beyoglu) Sofyali Sokak 9 near Tunel is a more upmarket “Meyhane” than the one above similar dishes to the one above but a bit more formal always full, reserving an outside table seems difficult if you are a visitor you may have to settle for inside €€
Boncuk, (Beyoglu) Asmalimescit Sokak is another recommended Meyhane the staff are not too pushy and it is reasonably priced.
Gedikli, (Beyoglu) Sofyali Sokak, is another Meyhane that always seesm popular with locals and the fish is good try the special of Sea Bass kebab, the prices are reasonable.
9 Ece Aksoy, Otelier Sokak No. 9 is a very modern looking place with some really different dishes, the owner is charming and it makes a great change from the more pushy Meyhanes in the surrounding streets. Go down Asmalimescit Sokak and it is in the last street on the right.
Montreal at the top of Asmalimescit Sokak is a cheap local bar, staff are very frinedly and the payment tables are fun for people watching.
Deguystasyon, (Beyoglu) Sahne Sok 41 (The fish market street) is recommended in a lot of books while the food was fine and the price OK but the service was truly appalling, try the one next door if you want to eat in that street.
There is a great local bar just across the road from the foot of Sahne Sok, very friendly and very cheap.
Lerb-I Derya Richmond, (Beyoglu) 6th Floor Richmond Hotel, Iskital Caddesi 445 the hotel does not prepare you for the restaurant on the sixth floor with the most amazing view. Get a window table and enjoy the food which unlike some of the other roof top restaurants does have a Turkish slant, very reasonably priced for the setting and quality of food but if you drink wine it may cost the same as the meal €€-€€€
The Pera Marmara Hotel has a roof top restaurant, highly recommended but very expensive, it also has a terrace bar area which probably has the most spectacular views because of how high up you are - go and soak up the view and the cocktails !
Lokanta (Beyoglu) Mesrutiyet Caddesi 149 is very highly rated in summer it moves up to a roof top location next door and also has spectacular views
Ciya (Kadakoy Asian Side), Guneslibahce Sk, 43 What ever you do get on a ferry and go over to Kadikoy a very relaxed, almost studenty area which has a restaurant with the reputation for doing the best Turkish food in Istanbul. There are actually 3 Ciya restaurants all specialising in different aspects of Turkish Cooking they are unlicensed and the menu is in Turkish, they now have an English version but don't speak much, but don’t miss out and the prices are incredibly cheap for the quality, choice, service and surroundings.
Safir (Ortakoy) Degirmen Sok 16, a good choice if you visit the lovely area of Ortakoy a wide range of dishes and good service $$
If you are doing the sites in Sultanahmet it is more difficult to find somewhere for a drink such as a beer, there are lots of cafes selling cold soft drinks, If you want a beer then check your guide book there are places but one to avoid is the Sultan Pub. It is in a prime site near the Blue Mosque and looks very welcoming, unfortunately they have no prices for their draft beers on the menu so charge the same as a vastly expensive imported beer. Go somewhere else this was our only disappointment in Istanbul.
Yesil Ev, Kabasak Caddesi 5, is a lovely hotel with a garden which does drinks and food, it is not cheap but it is a loevely relaxing spot to visit.
Onnumara, on the Galata Bridge right hand side going from Beyoglu if you are tired of being dragged into the various places on the bridge try this one brightly coloured cushions and beanbags very chilled out and great views
Pano (Beyoglu) Hamalbasi Caddesi 26, an old fashioned Greek style restaurant and bar lovely place to stop for a drink or to eat, these days seems very quiet.
Victor Levy (Beyoglu) Hamalbasi Caddesi 12 is a similar establishment to Pano and both make a welcome change from some of the more frenetic streets nearby.
360 (Beyoglu) Iskital Caddesi, 311 at the top of what is an apartment block and with a roof top open terrace this bar and restaurant is the place for a cocktail and a view also the restaurant is very popular with a fusion type menu.
Cezayir, (Beyoglu), Hayriye Caddesi, 12 (Behind the Galata Lycee), keep going down several flights and find yourself in a magic garden of a bar and restaurant with indoor spaces for the cooler weather and if you exit at the lower level you come out into a street lined with restaurants and bars know as French Street.
KV Café (Beyoglu) Tunel Gecidici 10, in an arcade opposite the Tunel Funicular is this lovely Bar and Café you shouldn’t miss walking through the arcade which will take you into into a couple of streets full of bars and restaurants from the very smart House Café to the basic Badehane.
Enginar (Beyoglu) Sah Kapisi Sokak 4A, near the Galata Tower if you visit the Galata Tower or are brave enough to walk up from the Galata Bridge to Tunel then you must stop at Enginar, a lovely bar and restaurant with great relaxed service a perfect place to chill out. Food looks good and teh staff are very friendly.
Ozsut (Beyoglu) Iskital Caddesi No 15 (Taksim Square) for the best cakes and iced coffees in Istanbul there are other branches around the city this one has a roof top terrace
If you have crossed over to the visit Kadikoy on the Asian Side then before or after you have eaten in Ciyak visit the Bar Street Kadife Sokak which has some amazingly laid back bars very welcome after a day of the sites in Sultanahmet.
Most of the sites are the ones that everyone knows the Topkapi Palace, a tip is, as you have to queue and pay separately to see the un-missable Harem do this as soon as you enter then see the rest of the palace at your leisure.
The Haghia Sofia Mosque and the Blue Mosque are also required sites to see along with the Grand Bazaar which is less frenetic that expected, be prepared to haggle and stop for tea or soft drinks at the Fez Café in the middle.
Yerbatam Sarnici, just round the corner from the Sultanahmet is a wonderful place to visit.
The Istanbul Modern is well worth a visit, an excellent permanent collection of Turkish art and special exhibitions, the tram stops about five minutes walk away.
Take time to visit Ortakoy a lovely part of Istanbul just under the bridge linking the Asian side and the European side and from there are hour long cruises along the Boshporous up to the next major bridge crossing these go from a pier to the left of the Ortakoy Mosque if you facing the water buses go there from Taksim.
Probably the first time I have recommended a Shopping Centre but if you want to see a spectacularly designed shopping centre which looks like an outdoor canyon then visit Kanyon it is on the metro at Levent the stop is Levent as oppose to Levent 4 the end of the line. The shopping centre is linked to the station.