Where to visit from Nice

See https://www.ricksteves.com/europe/france/french-riviera for a start, with map and links. If that looks good, then Rick's Provence & French Riviera guidebook fills in lots of details.

For taxis, see http://en.nicetourisme.com/taxis.

Thank you so much, Laura! So many beautiful places, so little time!

If you like twentieth-century art I would strongly recommend the Fondation Maeght art gallery in St Paul de Vence and/or the Matisse chapel in Vence. Another interesting trip is to take the Provence Railway up to Entrevaux, which is a fortified village that is much less touristed than the ones near the coast. The scenery along the railway is pretty good as well.

Around Nice are several wonderful small towns. Bus to each one was one Euro each way when we were there. Monte Carlo, Grasse, etc. Wife loved perfume shop and plant in Grasse.

Philip, which would be the better day trip, Vence answer St Paul de Vence or Entrevaux?

Do get Rick Steves Provence And The French Riviera. His general France book has much less information about this area.

There are many many options, so read about them and see which ones appeal to you. Off the top of my head, in my ten nights in Nice I saw Monaco, Menton, Villa Ephrussi, Eze Village, La Turbie, St. Paul de Vence and the Fondation Maeght, Haut de Cagnes and Renoir's house (this town was a real highlight), Cannes (which I found quite different from how Rick depicted it), Juan les Pins, and Antibes. I'm forgetting a few as well. Many of these were on combined trips (for instance, Monaco and Menton on the same day).

Trains along the coast run twice an hour, until about 11:30 PM, and are cheap. Buses along the coast from Nice east to Menton run four times an hour and are even cheaper. Buses along the coast from Nice west to Cannes run two to three times an hour, but take much longer than the train. Buses to higher destinations (like Eze, La Turbie, and St. Paul de Vence) are less frequent, so you need to check schedules, and they are reduced or non-existent on Sundays - plan ahead.

Rick's book has all the logistical details for visiting these places, and more (such as the inland train referred to above, which I didn't take).

Villefranche-sur-Mer is great. Do not miss Villa EphrussiRothschild gardens. Eze is great, the high village, take the bus. Menton via train. So much to see!

Not sure how much time to allow in these places. Will it work to do Villefranche sur Mercedes and Eze in one trip and Monaco and Mentone in another? Antibes and Cannes in one trip and Vence and St Paul de Vence in another and still have time to enjoy these places without being rushed?

The best thing to do is play it by ear. You will find you respond to some of these places and not others. If you are seeing a designated sight (like the Villa Ephrussi or Fondation Maeght), then of course you need to allow time for that. If you're just going to a place to walk around and see it, you need as much or as little as that takes - which can't be predicted in advance. For instance, I didn't care for Villefranche at all - I maybe spent a half hour there, tops. On the other hand, I enjoyed walking the parts of Cannes away from the beach, and spent longer there than I had planned (or Rick feels would be needed, just to see the glamour zone near the beach and the Carlton Hotel). I liked Monaco so much I returned a second day (there are more sights than Rick lists - I saw the Prince's car collection and the Princess Grace Rose Garden on my second day, in addition to the aquarium and the Jardin Exotique I had seen the first day).

A good plan is to start by going to a town that interests you. If you like it, linger. If you don't, you can move on to one nearby (you've listed some logical pairs, like Cannes and Antibes; I saw Juan les Pins in between these).

Ok, I wrote Villefranche- sur-Mer but my tablet thought it knew better. Yes, playing it by ear makes good sense but as a starting plan would those combined stops sound workable?

I can't say whether Entrevaux or the Vences would be better for you because it depends on your favourite era of art/history. It is possible to do both the Vences in one day by public transport as they're on the same bus route, although the buses can be very crowded in high season.

The reason why I suggest Entrevaux is basically because I hate Eze so much - I think it's the definition of "tourist trap".