I second the idea of not stopping if Provence is your destination then go there and maximize your time. Lyon is fine little city that is on the train line and I might suggest it if you had an extra day or two but it sounds like you really don't and while it's French it is not Provence.
To experience Provence I would make sure you get at least one market day - check which days of the week you have and coordinate to be in at least one city on market day. The main mid-size cities in Provence are Arles and Avignon and these are the two that are most often used as bases for exploration. Avignon is the best connected by bus and train and also for any organized tours as well. If you really have a specific Provencal topic - wine, food, art, ruins - then arranging to get a good guided tour and/or classes is often worth the money to really dig into a subject. Arles is great city (that I prefer to Avignon for visiting) with Roman ruins and a heavy van Gogh influence.
Arles market days: Wednesday but bigger one on Saturday.
The top small cities usually mentioned are St Remy - super classy in a refined way - and the picturesque L'Isle-sur-la-Sorgue which is the most accessible of the Luberon hill towns with a famous market day. Aside from the rest of its charms St Remy has the asylum where van Gogh was committed and he returned to painting and Gallum the ancient ruins just outside town. St Remy may be challenging to get to via public transportation in the off season.
St Remy market day: Wednesday
L'Isle-sur-la-Sorgue famous market: Sunday
I very much liked Vaison la Romaine as small town but it is a bit out of the way and unless you're really into Roman ruins it's probably too far to bother with. There are more charming Luberon hill towns past L'Isle-sur-la-Sorgue - these are the ones from A Year in Provence - but have limited public transportation options. Les Baux is another city with a ruined castle and some other touristy sights that can difficult to get to in the off season.
Vaison la Romaine market day: Tuesday
Wine is obviously a big draw to this areas with the town of Châteauneuf-du-Pape one train stop north of Avignon and several other slightly less well known wine areas scattered around as well.
Nimes is the biggest city in the region and has some sights but people are usually looking for more quaintness and less modern sensibilities that a larger city brings.
I'd recommend gathering some more information and then coming back as you have more questions. It's helpful if you layout your interests, must do things, favored transportation methods and the days you'll be there for people giving advice to be as specific as possible.
Happy planning, sounds like a great trip,