I don't know if you have time but I recommend to take a bus from Nice station to Eze Village (line 82 or 112, €1,3O one way). take around 1 1/2 hrs in Eze village (including the exotic garden). you can ask also at the tourist office organized a tour (€6 each). You can also visit the perfume factory Fragonard (one hour), it's free
We ate at a place that translated to "the place of eagles" and it had a picture of B Clinton standing in the place from a couple years before
After take a bus , 20 min, (line 112) to Monaco and visit Monaco (palace, oceanographique museum..) and Monte Carlo (have a look the Casino square). Monaco/ Monte carlo is a small country, so you can walk in Monaco
Monaco and Monte Carlo, I recommand 3 hours
after take a train or bus line 100 directly back to Nice
Check out Holidaytaxis.com - they will be able to give you a price for a taxi from one to the other, and if its not available on thier site you can email them and they will get you a price.
Try this website for instructions -
We used it to go Ville France to Monaco by train only 8 euros return it was easy and so cheap. Its about 25 mins on the train from Nice station and is a costal trip so quite pleasant. Just remember shops there close on Sundays and if the Grand Casino takes your fancy watch the dress code and opening times but well worth a visit just to see the wonderful building and the views over the bay from that side.