10 days in Dordogne

We stayed in Beynac last Fall and loved it. Here's a link to my Trip Report if you're interested. https://community.ricksteves.com/travel-forum/trip-reports/trip-report-part-2-hills-and-castles-dordogne

*we also stayed for a couple of nights in Rocamadour and was disappointed.

I suggest you focus on finding accommodation that suits your needs, taste and budget but offers something a little extra. With 10 days, you could consider two different stays, maybe an apartment (or hotel if that's your thing) in a bigger market town and a house/guesthouse/farmstay/inn in a more rural setting. Having a car allows you to stay just about anywhere.
Depending on when you are going, take a look at what town has the Felibree that year. This is a festival in early July, and the towns decorate with strings of flowers (including artificial ones that stay up for months afterwards). We happened upon this while driving through Saint Cyprien in September 2018. This year, it's in Sarlat-le-Caneda.

I feel like I need to preface this by saying these are my impressions. Other people have different impressions. Mine may inform your choices but you might also form a completely different opinion.

What time of year? Year round Sarlat de Caneda is probably a good bet. It's a very charming town with a fairly good supply of both lodging and restaurants. It's a good base for the area. In the more crowded months, it will be somewhat overflowing with tourists.

Another suggestion would be Domme. It's a Bastide (fortified village) just up the Dordogne from Beynac, La Roque Gageac and Castelnaud. If you're there off season (Nov-Feb), however, it might feel deserted, and restaurants might be closed.

I wasn't thrilled with Perigeaux. It's a pretty large town, not really nice. Two churches there are built in a Venetian style that's interesting but, for me, not enough to return.

Rocamadour is probably the bottom of my list. It's a Catholic tourist trap. I like Catholics, but I'm not Catholic. If you visit Rocamadour, you'll see what I mean. I felt is was run down, much less clean than almost any other village in France, and the one main street is lined with shops selling Rosaries, statues of saints and similar souvenirs. Places I visited once and wasn't motivated to return include: Les Eyzies, La Roque St. Christophe, Figeac. They are all okay and might be good stops depending on your interests.

If you're in the area for 10 days, you can see a lot. I'd probably break it into several stays, to use as bases to see the area, to reduce driving time.

The main sights on the Dordogne are great, but they also draw big crowds. I'd consider some sights toward the Lot Valley as part of your plan. Some of my favorites include: Cordes-sur-Ciel, Fortress Royale de Nejac, Saint-Cirq-Lapopie, Turenne, Autiore, Cajarc, Chateau de Cenevieres, Conques, Grotte du Peche Merle, Gouffre de Padirac. Some of these are just small nicely preserved medieval villages that are worth a look around and lunch at a cafe. Others have lodging and might serve as a base.

We stayed in Perigueux in July and absolutely loved it. We always prefer staying in larger towns with more amenities (Basic Fit, E LeClerc, French Domino's Pizza, bakeries, shopping) and a more authentic (less touristy) feel. We stayed in a normal (old building but newly renovated) apartment about two blocks outside of the old town. The city center was beautiful as was the waterfront. We chose Perigueux because we wanted to be centrally located to conveniently go north to Oradour-sur-Glane and Brantome, plus near the highway to get back to Bordeaux quickly to return our rental car and fly home.

In 2023 we stayed for 10 days (there were 7 of us) and I found a terrific house for us at gites-de-France. We have used them to find lodging for even shorter stays in different parts of France and have always been more than satisfied. They have been around longer than AirBandB and do things right. Our place was quite large due to the number of us, but they have everything from small cabins to apartments to houses. We were in the countryside between Vitrac and La Roque Gageac, in a peaceful place next to the river, with a pool and modern kitchen and caretakers on the grounds. It was a short drive (no more than ten minutes) to a nearby town for the bakery and grocery store. Sarlat-la-Caneda was 15-20 minutes, La Roque Gageac 10 minutes, Domme 20 minutes, about 20-25 minutes to Beynac and Castelnaud-la-Chapelle, 30 minutes to Les Eyzies (Font de Gaum) and the same to Lascaux IV, plus 10 minutes to our Vitrac put-out for kayaking. We never had time to get to the eastern parts of the Dordogne. alas. Next time!
Do try Gites-de-France for lodging. Our place was centrally located for all we wanted to see and do and all we had time for. Plus it was nice to return to our "home" for the evening, sometimes grilling our dinner or cooking inside. And each day one of us went to the closest bakery for our breakfast croissants and other goodies! Yum!

P.S. Travel Boss is correct about Rocamadour being a tourist trap, at least the lower town seems to be. The church at the top of the hill is interesting, but IMO not worth the drive. (And I must add that it is not really a Catholic tourist trap, but an over-touristy and tacky souvenir lower town.) It's nothing to do with the Catholic history of the place or the church itself. Still, definitely not worth the time.
Travel Boss makes some good suggestions re the Lot Valley also. I would take some time to check out some of the towns. Google "Les Plus Beaux Villages de France". Many of them are in the Dordogne. And seek out market days, always a nice way to spend a morning.

Personally, I always look at a real map of a place I'm visiting, to see the big picture, area-wise. Then I have some reference points about distances between places and I can plan better. I go to viamichelin.com to ascertain drive times, whether near or far. Way back in 2023 I did a trip report on our stay there. It's from June of 2023 and titled "Just Returned from Four Weeks in France...Continued". Scroll down to the part beginning The Dordogne Valley. Maybe you can find something useful there.

I'm glad you have ten days there. You won't be bored! Have fun!