I've never beed to Nice so I don't know if this is in a good location. Let me know if you were happy with your stay or if you have any other suggestions. This one is 65 euros including breakfast.
http://www.nicehomesweethome.com/
The reviews on trip advisor looks good. I was in Nice in the first week of september. The location looks good- convenient to the train station and Jean Medicin Avenue.