There are frequent buses from the Airport to Nice, one runs to teh Bus Station (Gare Routiere) the other less frequent to the Railway Station (SNCF) you have to buy your tickets first and there is an office just outside the terminal.
Nice has a new tram which runs from the station and is very useful, runs late you can buy day tickets/
No particular recommendations but I would suggest that being near to the old town and the port area is preferable to the station side of the city it can seem quite a long way crossing the city from that side to the old part , the new tram helps.
Hotel Villa La Tour, is a basic hotel but with good reports and in a great siutation two minutes from the Bus Station and just on the edge of the old town.
Le Safari, 1 Cours Saleya rated as the best of dozens in Cours Saleya terrace tables booked by locals so book or get there early the Cascade Nicoise as a shared started to be recommended loads of choice €€
Papayou 35 Rue de la Prefecture Modern friendly restaurant with a different slant on Nicoise dishes all very well cooked € to €€
Restaurant L’Escalinada , 22 Rue Pairoliere Get a table on the terrace, loads of local specialities and jugs of wine cash only, loads of free nibble to start but no longer as cheap as it was €€
Lou Pilha Leva, Place Centrale queue for your food and take it to one of the outdoor tables and get served with drinks by the drinks part opposite it’s local special is “Socca” pancake also salads & hot foods incredibly cheap €
Chez Palmyre, 3 Rue Droite 4 course set lunch ( although one course is the vegetables for the main) great old fashioned local place very friendly stick to the house wine and it is incredibly cheap
Vin Sur Vin, 18 Bis Rue Biscarra Wine Bar/Restaurant fabulous food and wine cave where you choose your wine speciality is meat but everything from starters to cheese and wine excellent as was the service book in advance €€ to €€€
Wine Bar de la Tour, Rue de la Tour - nice place to sit out and soak up teh atmosphere.
Culture
There are lots of museums and galleries although they are mainly in the suburbs so a bus map is a good idea.
Places to visit take the train along coast to Monaco & Ville Franche which is a lovely setting for lunch
Metro excellent to use to and from station but be observant
Hotel Alize 35 Quai de Belges available on www.venere.com or direct http://www.alize-hotel.com/english/hotel_tarif.asp rooms with view of the old port are a must as you will see from the reviews the rooms are basic but the reason for choosing it is the location and choose a front for the amazing view. There are other hotels on the Quay now but they are more expensive.
La Part Des Anges, Rue Sainte 33 just behind the Quai Rive Nueve at the old port it’s a wine bar and restaurant with great daily specials and the wine list on blackboards behind bar they always have suggestions for daily specials so good we went back twice €€
Toinou off Le Canabiere 3 Cours Saint Louis Marseille institution for seafood great platters of oysters, clams & langoustines plus moules & frites €€ to €€€
504 Marseille Restaurant Familial, 24 Place Aux Huiles Excellent Moroccan Restaurant Good atmosphere and great food € to €€
Place Aux Huiles has many recommended restaurants and bars great place to sit out.
Cours Julien up the hill behind the port has loads of places to eat particularly pleasant at lunch time
Lots of bars do free tapas in the early evening and some do 2 for 1 drinks
Aix en Provence Fabulous elegant town with great markets very cheap lunchtime restaurant near the market Le Carillon Rue Portalis, easily reached by train
Cassis a beautiful sea side town with loads of places to eat and boat trips to visit the Calanques (inlets that only accessible from the sea)