If you could only see one of these villages which one would you go too?
Eze-le-Village! There are 2 Ezes, you want to go to the one on the Middle Corniche, not Eze-Bord-de-Mer on the coast. If you're not driving, take bus 100 from the Nice bus station to Eze-Bord-de-Mer; and from there, bus 83 takes you up the cliff (and I mean cliff) to Eze-le-Village (your destination). Plan on a wait for the bus unless you hit it just right. An alternative is to take the train from Nice to Eze-Bord-de-Mer, then bus 83 as above. A 3rd way, and maybe the best but I didn't know it at the time, is: bus 82 or 114 goes directly from Nice to Eze-le-Village, so I'm told (verify the bus # at Nice bus station b/c these #s may have changed). A 4th way: get to Eze-Bord-de-Mer by one of above methods, go to the bus stop and check when next bus 83 is, if you don't want to wait that long, near the bus stop there's a phone # for local taxi service; last time I did this (in 2007) it cost €25 - €30 one way, good if you can share the ride with someone. MOST IMPORTANT: Watch "To Catch a Thief" before you go, it was filmed partly in Eze-le-Village, starring Princess Grace when she was just a Hollywood actress and before she met Prince Rainier. She was killed in an auto accident on the Corniche highway not far from Eze, so be careful if you drive it, don't drive back down to Nice at night after a few drinks.
When you're in Eze-le-Village, for one of those unforgettable European moments, a spectacular "terasse panoramique with glass of wine" experiences, see if you can find the Chateau Eza. This is a luxury lodging built on the Eze cliff, used to be the winter getaway of one of the Scandinavian royal families. It's a top of the line French boutique lodging property. Walk into the lobby with confidence, as if you're staying there, and ask the maître d' to seat you on the "public part" of the outside terrace. He may tell you it is only for guests--but if you're reasonably well dressed and can ask in French--he'll probably show you to a small terrace with an absolutely jaw-dropping view. A glass of wine is pricey but it will be one of the better investments you'll make on your trip. Rumor has it that if you get up and look over the railing at the truly for guests only lower terrace, you just might see somebody famous.