I will be staying three nights in Nice. Please help me plan my stay. What other places should I go?

Three nights gives you two full days, barely enough time to see Nice so I would skip day trips this time.
Musee Matisse, Mussee Chagall, Promenade des Anglais, Place Massena. Mussee Massena, Old Town, Parque du Chateau.
If you have to do a day trip, take the bus east to Cap Ferrat, visit Villa Euphrussi and the village of St-Jean or take train west to Antibes.

Try reading this: http://www.fodors.com/community/euro...ern-france.cfm

I would definitely get away at least one day. There is no reason why you have to see every sight in Nice before you get a broader impression of the Cote d'Azur. Like Happy Trvlr I think Antibes is a nice choice - - it was a lovely market, the Picasso museum, and has a completely different vibe than Nice, which is a busy place. Walking up through the old town in Cannes is interesting too. Taking the train a few minutes to Villefranche sur Mer is great for swimming. Grasse, St. Paul de Vence, and even slick old Monaco are worth considering. Mix up the trip the way you feel, and then there will be plenty more to see - - in Nice and outside Nice - - to justify another visit.

I loved the Chagall Museum.

I loved the Matisse-designed church up in Vence above Nice. Nice does have an on-off tour as I recall, so you can do that. It's not an especially interesting city IMO. The outdoor market (which I think is open every day) was lovely, walking a bit on the Promenade Anglaise (the seaside walk) was nice. We didn't feel bad leaving after a day or so. St. Paul de Vence is close and is a really gorgeous little walled town (Vence is next door--where the Matisse church is) famous for La Colombe d'Or restaurant where Picasso painted some murals. The Maeght Foundation (Fondation Maeght--pronounced Mag in French for some reason) art museum is really great, which is right in that area in the hills above Nice. Nice proper is probably the least pretty place in the area IMO.

I basically agree wtih happytravlr in terms of things to see in Nice, they have a markets down on cours Saleya some days in the Old Town, see http://gofrance.about.com/od/nice/ss/coursselaya.htm

YOu can easily get to Antibes by train, if you want, or take the bus to Grasse, as well as Vence.

FYI Maeght is not pronounced basically "Mag" in French for odd reasons, it is a proper name and that's the way the family pronounces it, that's all, it doesn't have anything to do with French. It is Flemish, anyway, and they often drop ending t's in Flemish.