I know there are lot of things to see in Provence and French Rivera. However, I have limited 5 day in the area and travel by train only. Please help me get the best out of these two places by recommend your favor cites/villages and hotels/restaurants in these two places. Thanks.
provence is best with a car, so you should just see the big towns, say avignon and arles with train (bus is unreliable in this area, and avignon has a long distance bus barn if you do want to ride bus). rivera is perfect with train or bus. nice has a long distance bus barn you can ride to small hill towns. 5 days are not very much time, but you can at least check out antibus, nice, and monaco, and possibly do the train hopping to see another coast town, or a hill top village.
I agree with David about a car. While there are lots of trains, and buses, I found they often did not meet my scheduling needs. You can get to Avignon, Arles, Nice, Marseilles by train...but you may not have a lot of time to explore both areas. You may want to focus on one particular area, rent a car, and explore from a central base. I spent three weeks in Provence last spring mostly without a car. Although I loved the area, a car would have given me more flexibility in where and when I went.
What time of the year? It makes a huge difference. Generally you will find better transportation in the Cote d'Azur (Riviera) than in Provence. 5 days sounds pretty good to me for one or the other, very cramped to try to do both. But, again, when?