Very tentative itinerary Paris-Provence-Nice
 

We have decided to head to France for our New Year’s trip. I have been to Paris before several times but neither of us has visited any where else in France. So preliminary plan is fly to Paris, take the train to Provence stay 4 nights then head to Nice by train to spend 3 nights including New Year's eve then head back to Paris by train on Jan 1st to spend 3 nights. While in Provence and Nice we plan to rent a car whenever needed to tour neighbouring villages. I am reading Stu’s report on Provence and Riviera and getting some great pointers. Ok, feel free to pick apart our plan and please guide us with these issues:
1-Which base in Provence given that we want a place reachable by train, since we will be flying and taking the train on same day we want somewhere where we don't need to rent a car to reach.
2-Hotel recommendation in Provence. We are open to any suggestion, either small or big hotel as long as it is clean and centrally located. We have settled on Windsor Nice, I have emailed them and gave us a rate of 120 euros for comfort room w/o breakfast.
3-hotel recommendation for Champs Elysee, so far we like hotel Keppler but it is a bit expensive 260 euros/night.

All help is appreciated
Thanks a lot
Alia

I would choose St-Rémy as a base for Provence if this is your first trip there. It's a short ride from the Avignon TGV station, is large enough to have things going on in the dead of winter, is close to many of the sights you'll presumably want to visit, and has a nice selection of hotels and restaurants/cafés, etc.

Why do you want to be on/near the Champs Elysées? You'll pay a premium to be in an area of Paris that is far less interesting than many, many others.

Pick up your car in Avignon and you can return it at the train station when you leave. With a car you can base yourself anywhere. St Remy is a good choice to see that area, the hill towns and the Pont du Gard