We will be staying in St Remy, Provence for 9 days, with a car rental. We then plan on 4 days Riviera area,so far thinking of basing in Villefranche sur Mer. Thinking of returning the car rental in Avignon and doing the Riviera by train & bus. Wondering if the best way to get to Villefranche is by taking a train from Avignon-Nice, then bus or is there an alternative route? We plan on exploring Nice itself on our last day before flying back home from Nice airport.
I might misunderstand your question, but the trains from Nice to Italy run through Villefranche. Any local train will stop there. Train from Avignon to Nice - easy.
"Wondering if the best way to get to Villefranche is by taking a train from Avignon-Nice, then bus or is there an alternative route?"
You can take a train to Villefranche-sur-Mer from either Avignon or Nice (you go through Nice to get there).
Many, however, feel the bus from Nice is more scenic.