You should look in the Carre d'Or and the few blocks around Place Massena. This is roughly the area bordered by the Promenade des Anglais, Boulevard Gambetta, Boulevard Victor Hugo, Rue Alberti, Avenue Felix Faure/Promenade du Paillon (or within a block or two of these boundaries). This will keep you close to the main train station, the Old Town, the Beach/Prom and both main tram links. There are tons of restaurants, groceries and boulangeries/epiceries (deli/takeaway) in these areas. You will more likely to find places with AC (verify if it is in every room) and elevators. Be sure to check beyond the main resellers to the local agencies. The city has worked to remove unlicensed listings, so capacity is a bit down.
The Port is another potential area, it just places you further away from the main train station (you can take the tram, and then transfer, or walk to line 1) and most sites (market, beach, museums). Also, in high season, the trams can get very packed so it is nice to have a good walkable option.