jphbucks,
What often causes confusion about the Dordogne and where it’s actually located is that the name “Dordogne” refers to several different things, thanks to French bureaucracy for the mix-up. It can mean:
The Dordogne River
The administrative department of Dordogne (Department 24)
The Dordogne Valley
The Dordogne “terroir,” which is essentially the Périgord region.
To make things even more complicated, I’d add that in terms of public transportation, Sarlat and the surrounding area are part of the Nouvelle-Aquitaine network (the same one as Bordeaux), while all the other areas fall under the Occitanie region, which manages a different transit system called the liO network. So, if you're trying to get around without a car and find the right transport schedules, good luck! ;-)
But I’m guessing that what you’re looking for as a tourist is the version of the Dordogne described by let’s say, Rick Steves. The one with the caves, castles, villages, canoeing, scenic landscapes, and farmers' markets. If that’s the case, Sarlat is actually just in a small area located more toward the west.
The thing most North American visitors don't realize is that you can find all those classic "tourist" highlights across a much broader area, especially east of Sarlat and into the Lot River Valley. This includes at least the Lot department and the Quercy region.
You'll find this information in all good travel guides. For example, the Michelin Guide:
https://cartovia.com/en/products/guide-vert-perigord-quercy-dordogne-lot-michelin
https://www.amazon.fr/Guide-Vert-P%C3%A9rigord-Quercy-Dordogne/dp/2067244914
Or the Rough Guide:
https://shop.roughguides.com/book/the-rough-guide-to-the-dordogne-the-lot
Fortunately, there are a few people on this forum who have ventured further east and south and can confirm this.
To give you an extreme example: if you look at this tourist map of the Dordogne Valley, Sarlat is so far west that it's actually hard to spot.
https://www.cartographik.com/Dordogne%27s-valley---touristic-map