Burgundy region by train?

You can easily get to Dijon or Beaune by train. We liked Beaune. We stayed at Hotel de France for a budget property. The restaurant there is excellent with well priced Burgundian food. We had a car. We drove on the Route des Grand Crus from Beaune to about Dijon which was lovely. You could pick up a car in Beaune or you can rent bikes to visit wineries or take wine tours.

We took the train from Paris to Dijon in Oct 2017 and stayed at the Grand Hotel La Cloche. It was an easy walk from the station and was a lovely place to stay, perfect location right across from the tram and the city center. We did a wine tour with a small group to Beaune, so much fun, gorgeous scenery and amazing wine, in fact we ended up taking the train back to Beaune for lunch on our last day. We shy away from renting cars and had no issues at all getting around. I will say this though- I would spend the entire time in Paris if it's a first time visit and you only have one week. Truly, there is just so much to do and when we go we always wish we could stay longer.

Train to get out there, wheels (car or bikes) to get into the beautiful countryside.

It's largely rural and not well served by rail.

I recommend reading a few guidebooks and picking your top sights. Then get a map and string them together into an itinerary.

Beaune is fun and friendly but not worth 4 nights. Vezeley is stunning, Fonteney Abbey worth a visit, Semur a lovely town.

I would agree that Beaune may not have enough for four nights. If after reading a guidebook and doing some research you do decide on a car, I would add Noyers sur serein, a beautiful medieval town, to your list of "to dos".

Beaune would be a good base for four nights if you don't want to be changing hotels, and if you have a car to get around. It's close to the intersection of two autoroutes, and has a ring road to get you in and out of town in any direction. Plus quick and easy train to and from Dijon. Adam is right about Vezelay, Fontenay, and Semour-en-Auxois, and there are many other delightful towns and villages. Beaune itself has a couple of good sights, most notably the beautifully restored 15th-century hospital. It also has a lot of tasting rooms if you want to try (and swallow) different wines without then driving.

If you rent a car, you'll be able to visit some the quaint villages, beautiful cathedrals and impressive chateaux of the region. If you decide to rent, stay in one of the small towns, so you aren't driving unnecessarily through city traffic in and out. Also, have GPS. On the other hand, if you plan to do a lot of daytime wine tasting, you are better off without a car. The blood alcohol limit in France is lower (0.5%) than in the US (0.8%), so more than one glass can take you out of the driver's seat.

I second Adam's idea reading guidebooks for putting together your itinerary and visiting for instance the places he mentiones. Training to Dijon or Beaune for exploring the area by car is not a bad idea. But Burgundy (and adjecent department Yonne) is huge, meaning a central place to stay is not always efficient, so best is visiting places on the way back to Paris and drop off the car closer to it, for instance in Troyes.

There are loads of lovely places, like to add a few like the already mentioned Noyers, Auxerre and not to miss Troyes, the latter to my opinion more beautifull as Dijon and Beaune. Further Guédelon, a medieval castle construction site using original building techniques.

Burgundy is wonderful and a car is necessary to make the most of the 3 days there. I hope you have been to Paris before if you are only giving it 2 days.

Here are some of the spots we visited in Burgundy; it is unendingly beautiful and we loved just driving around and following the signs that identified historic sites, monuments and towns.
https://janettravels.wordpress.com/category/burgundy/
We particularly liked Semur en Auxois and spent a week there as a base. The Fontenay Abbey is also a great choice if you want to visit an Abbey. On other trips we have stayed near Avalon and close to Vezelay and Auxerre staying at the country inn Moulin des Ruats. It has a very nice restaurant that draws from the area.

Thank you so much for all these responses, so helpful! We haven't even been to Europe before but didn't want to limit ourselves to just Paris. We arrive on a Wed morning and leave Tuesday afternoon. We read a lot of wineries not open on Sunday so we could do 2 days in Paris, go to Burgundy region and go back to Paris Sunday Monday.

I agree with others that train to Dijon or Beaune is a good start, but you probably want a car to really soak up the Bourguingon countryside. We've stayed in both of those cities multiple nights, but found that our favorite days were outside of the cities and in and around the vineyards, abbeys, and chateaux that are nearby.

The places mentioned are fabulous: Vezelay, Fontenay, Semur, Chateauneuf-en-Auxois. The RS guide has a couple of good driving tours for the region, one for vineyards/wineries and another for the countryside more generally.

I'm glad you've heard about the Sunday/Monday thing. Things do really close down. You're right that Paris would be better those days.