Is there some sort of day pass that would be suitable for travelling up and down the French Riveria area, jumping off for an hour or two at one town, then the next, then the next etc? In the stretch of area Menton to Antibies.
Train tickets for TER trains are flexible, and allow you to interrupt your trip. So if you for example start in Menton you could just buy a return ticket to Antibes, and then just hop on and off at leisure.
If you booked a return from Menton to Antibes or vice versa then would it be possible to do something like start in Nice, go to Menton, then down to Antibies, then back to Nice? You can go back and forth all day long?
no - the out ticket from Antibes to Menton is for travel in a continuous direction, with breaks of journey permitted in that day as long as it is always in the same direction. The return ticket, from Menton to Antibes works the same way... So you can board in Menton, get off in Monaco, get on again and then off in Nice and so on. You can't on that leg get off in Nice and go back to Monaco for example, you will be going backwards and that's not permitted.