Short, and straight to the point, off the top of my head here's a few tips from my stay in Nice that I hope can be helpful to anybody who is planning a trip there.
The airport is very close to the city, if you want to save the 6 euros that the 98/99 direct buses cost, take the number 23 instead, it's a city bus that costs 1.50 euro (or 1 euro if you buy a 10 trip card), it stops a few times along the way but it'll leave in the center of town in around half an hour.
As most people recommend, a day trip to Cannes and Monaco are definitely recommended. However, while the bus trip to Monaco is lovely (view along the coast is amazing) and relatively short (around 40 minutes), same cannot be said to the trip to Cannes. Mine took over two hours, and the bus must have stopped what felt like a hundred times along the way. If you don't want to waste 4-5 hours just to get there and back I recommend the train, although it's quite more expensive (6.60 euros versus 1.50 euro for the bus). Also, be aware that the 10 trip bus card does not work for either Monaco or Cannes.
Go to Ezè, it's really lovely and quaint, if a little crowded and touristy. You can get there using the regular bus ticket. It's small so you don't need to spend much more than a couple of hours, and it's totally worth it.
The old town in Nice is crowded with restaurants, almost every square meter is filled with them. They look and feel very touristy, and as person from Barcelona, I was very reluctant to eat in any of them as I cringe on a daily basis seeing the kind of touristy places that some people chose to eat when they come here. However, I was surprised to discover that most restaurants actually offer some fair value and you can have a decent meal if you look around. My point: if you're more of a foodie and wish to spend some time researching places to go eat, I'd say by all means go ahead, but if you find yourself wandering around the old town and you're hungry, you can still enjoy a decent meal.
Eat socca. This is a garbanzo (chickpea) pancake that is often eaten by itself as a snack. I didn't know about this before going but when I saw people eating it everywhere I had to try it and it's delicious.
Eat ice cream. Incredible variety of flavors, good quality - guess proximity to Italy doesn't hurt - decent price, good stuff.
Eat croissants. They really are better in France.
Coffee is a little expensive, at least for my standards - compared to Spain, similar/lower quality, doble the price.
The Russian church is lovely, a bit out of the way but worth a trip. City is not that large anyway and is very walkable.