Hi Keith,
That is a good budget for a long-term rental in Nice so you will have a lot of options. In the center, you could look around the Gambetta neighborhood, or near the Beaux-Arts museum. Try the Le Bon Coin website to get an idea of rental prices. Real estate expert Adrian Leeds is based in Nice and has great tips for the city on her website.
Tuula Rampont, IL France Correspondent