I love maps and always like to carry one with me to spot new routes and short-cuts which often turn out to be long-cuts because of the interesting places I come across!
You can get free maps of Nice from the tourist information offices next to the Gare SNCF and on the Promenade des Anglais next to the Casino Ruhl.
If you want to download a map in advance (giving you the fun of planning your days and doing some virtual exploring) go here for a straightforward map of the town centre including the Old Town – you can enlarge it so that you can really get to see all the little streets!
For a google map click here and print a copy to have handy on the plane so you can spot places along the coast as you fly into Nice!
thebestplaceinfrance 
I always carry that map of the town centre with me too, it’s fun to plot new routes and also v helpful when I lose my bearings in the Old Town!