I've done it a couple of times. Then walking up and around the town isn't even a mile. Maybe you guys parked some distance away from Eze proper and hiked to it?
EIther way, Eze is awesome.
We agree that Monaco is a waste unless you're some kind of high ball gambler.
Beach can be cool in the Cote d'Azur but agree that Nice isn't the best place for it.