Cote d'Azur - picking 2 home bases

I stayed 5 nights in Nice and day-tripped by train (cheap, convenient). My hands-down favorite was Ville-Franche, very small, good beach, not as touristy. Folks there told me that though it's a deep-water port and they get cruise ships, everyone takes the train to the "hot spots", hardly anyone stays in town for the day.

Some like Antibes; a few hours visit (excellent) was enough for me. Menton is larger and I liked it more but it's at the Italian border, so not as convenient as a base.

I also spent 3 nights with a car near Vence, in Saint-Paul. It had more of an urban feel than Menton or Ville-Franche. I only saw Saint-Paul in the mornings before the floods of tourists and in the evenings as the last of them were leaving and I loved it. It's very small, so I imagine it might not be a great place to visit as a day trip from Vence. Eze?

Without a car, I'd be reluctant to commit to more than 2 nights in one of the hill towns because public transportation is very limited. I liked Vence a lot; it had virtually no tourists the day I visited in May 2017, but I hit the town during the siesta period, which could have been a factor. St.-Paul-de-Vence was packed with tourists to a degree that was unpleasant for me (like Taormina in Sicily), but unlike Chani I didn't see it outside the day-tripping hours. There's some bus service between Vence and St-Paul-de-Vence (the bus coming from Nice), so you can stay in one of those places and visit the other, but after that, I don't know where you'd be able to go by bus without returning to Nice first.

I found a good bit to do in Menton (it has a couple of nice gardens), but the historic center was absolutely thronged with visitors. I wondered whether many of them were staying right in town, which would make it overrun at all hours of the day. But I don't know that that's the case.

I liked Antibes but only visited it for one day. I spent all my nights in Nice, which from a transportation standpoint worked out well. However, I can see that it would be nice to spend some time in a less urban environment.

Check opening hours of any sights you plan to visit very carefully. June isn't quite peak season on the Riviera, and you may encounter a few places that are closed two days a week during that month.

There is probably not enough of a difference between Antibes and Nice to split between the two, unless you just want to spend a couple of days dedicated to beach time (and then Juan Les Pins is another choice). They are very close together. Nice has better transport links, in general, and suits as an urban base. You could use Antibes as well, but it is not quite urban and not quite villagey, and you may find transport links less convenient.

I echo the sentiment regarding the hill towns without a car. It's possible, if you want to just stay put or relax by a pool, or plan small ventures by bike or local bus (in some routes, as few as 2x per day). Vence and St. Paul are reached by the same bus line from Nice (400). (SPdV is so close to the coast that taking an Uber down to Cagnes sur Mer is another option). There are also towns further to the west, like Mougins that are a possibility, or Eze, as long as you are not planning on a large number of activities. These small towns do get a lot of day traffic. I've stayed in SpDV at the end of June while still house hunting and the crowds are even more intense in summer (but do dissipate in the evening and early morning).

June is still considered in season, so you will not have problems with extended closures. However, museums and sights normally have a day of closure during the week.