next wk in nice
Chez Nounou is okay, but for the best Bouillabaisse in the area go to Tétou in Golfe Juan. The price is reasonable if you get the more authentic version without the langouste. If you don't have a car, it is a short walk from the Golfe Juan train station. Lunch is probably better and easier to get a reservation.
For dining in Nice I suggest Millésime 82, Flaveur and Keisuke Matsushima.
Actually, Bouillabaisse is not indigenous to Nice, the best really comes from Marseille and environs. One of the best is to be found at Chez Fonfon in Marseille.
I think in Nice, especially when you use the word "cheap" I would stick with a bourride or a soupe de poissons, a much less complicated fish soup but delicious and full of flavor nonetheless when prepared properly, and served with a lovely rouille and croutons.
For a great value you might consider Acchiardo in Vieux Nice, they make a terrific Soupe de Poissons as well as other Provencal dishes. 38 rue Droite.
P.S. Carnaval is on next week, don't do any driving anywhere in Nice, and if you get near the Promenade there will be some fabulous parades and costumes. Enjoy!