They're not as far away as you think, it's a reasonable drive/train ride between Avignon and Nice. If you get a chance, Nice, Cannes, and Monaco are all worth a trip, though you'd want to take three or four days to see them all properly. Elsewhere in Provence, there are nice Roman ruins, if you're interested in that. Definitely go to Aix-en-Provence and I'd also recommend Grasse, it's famous for perfumeries and gorgeous flowers. You really can't go wrong with Provence in the summer, but seriously, the coast is worth a trip, and you can do it easily by train.