Dordogne region

Sarlat makes a very good base. Prehistoric caves, lovely gardens, and a variety of chateaux nearby. Not to mention Wednesdays and Saturdays, which are market days in Sarlat. If you haven't already gotten a room there I would recommend La Villa des Consuls. It's a variety of accommodations under one management, all in the Old Town.
Between Sarlat and Amboise (closer to Sarlat) is Mortemart. It's a nice enough little village but the real reason for stopping there is to visit the ruins of a town (Oradour-sur-Glane) which was the site of a Nazi massacre. The town was then burned by the Nazis and left as it was by the French as a monument. Might not be your cup of tea for a vacation, but it was extremely moving when we stopped there.

If you are staying in a hotel, Sarlat is a great choice because you will have many dining options over the course of your stay. If you are looking for an apartment then I recommend Beynac for the following:

1. I love this place - we've spent 13 nights here between 2 trips: https://www.vrbo.com/343941
2. For food, the butcher and bakery in Beynac are out of this world
3. It is very easy to get in and out of Beynac. Sarlat has a lot of traffic and is slow to get through.

-Matt

This is our favorite part of France; we like to stay in small villages. If you are there in summer be sure to visit a night market for food and dancing and good times. Here is a less well known chateau ruin that we visited last fall:
https://janettravels.wordpress.com/2017/07/25/perfect-place-for-murder-commarque-chateau/
The markets, the food, the canoeing on the Dordogne (not the Vezere) river and the caves -- and the chateaux -- all fabulous.

Sarlat would be a good base, though as Matt points out it takes awhile to get in and out of the town. We stayed in Beynac at this B&B and were very happy with it. Beynac has several good restaurants, its own castle, and views of others.

Yes, Sarlat is a good base, but I'll agree with those who recommended Beynac. We spent a week there last year. The house we rented was fantastic, but the one Matt references also looks outstanding. I'm attaching the link to my blog covering one day of that trip, which includes a photo taken from our terrace. There's more about the Dordogne, including Sarlat, in other entries.
http://mainelywinenews.blogspot.com/2016/04/more-from-dordogne.html

No matter which town you choose, I highly recommend picking up a 3 pack of Bergerac wine on market day. I'm pretty good with wine and I'm quite confident that at 14 euros for the pack (you choose the colors) that's the best value I've ever experienced. The wine is really, really good in my opinion. The Rose is my favorite rose I've ever had. The pork products and the walnut desserts along with the Bergerac wine are amazing. The duck and fois gras are great too, but overshadowed by the pork ribs and other bbq meat. On our first trip we we're pleasantly surprised. On our 2nd trip we bbq'd with rose every night.

We also stayed in Beynac and loved it. We stayed at Le Petit Versailles b&b, a very lovely country home. We went into Sarlat several times, but are glad we stayed in a village near the river.

I can't pass up the opportunity to praise Le Petit Versailles in Beynac. I could compare the pros and cons of Sarlat vs Beynac and come out pretty even, but if you're staying in Beynac you really should try to book at Le Petit Versailles. We love this place. The house itself is quiet, with nice views. The hosts are wonderful and Mme Fleury puts on an absolutely scrumptious and plentiful breakfast. It's the best breakfast I've had at a B&B.

Our first time there Spring 2016 and loved it. Stayed at a B&B, manoir de la Malartrie, in LaRocque Gagneac (excuse if misspelled), one of France's "Most Beautiful Villages."....also recommend you visit that site if you haven't.
Wonderful hosts at B&B with the best breakfast spread ever....just check out the reviews on TA and you'll see the setting and details on this terrific place. Sarlat is busier...we prefer the quieter villages with B&B's or small boutique hotels. Bon jour!