We stayed at Les Cordeliers, right on the square in Sarlat: http://www.hotelsarlat.com/bedandbreakfastsarlat/. It is run by a couple of Brits and they have a great breakfast and rooms. We did not have a car, but he mentioned that there was free parking nearby. The website still says that toward the bottom of the opening page on the left.
We were in Room #6 at the top of the building. My husband hit his head on that curved beam only once while we were there. The prices may be a little high for you, but don't hesitate to mention that you are traveling alone. At that time of year, they might give you a reduced rate.
We were able to easily walk to places for dinner nearby and loved walking after dark in the gas lit part of the town. Most of the lights had Coleman lantern style flames, but we did see a few that had real flames without the little socks over them.
We spent only 2 nights, but we had lovely dinners at Le Bistro de l'Octroi (http://lebistrodeloctroi.com/welcome/4581823313) and Auberge de Mirandol (http://www.restaurant-auberge-mirandol-sarlat.fr/mirandol-fr/Les_Lieux.html). I skipped the intro on the Auberge because of the exceedingly annoying music. It had a flying British flag you are supposed to click on for English, but I couldn't get it to work, so you will be stuck with the French.
We didn't have nearly enough time to spend there that trip. I'd go back in a heartbeat. We were there in mid-October. My pictures show my husband in rolled up long sleeves and our tour guide, Phillippe (http://allophilippetaxi.monsite-orange.fr/) has on short sleeves.
You can find temperature averages for towns nearby here: http://www.weatherbase.com/weather/city.php3?c=FR&name=France. Just check your map, click on the name of a close by town and you will get a chart with lots of weather data.
I'd use Google Maps Directions to get the kilometers (start thinking in km) as well as directions that you may or may not use depending on your sense of adventure. Directions will give you alternative routes with slightly different distances and times. Just keep clicking on the + to get more detail and click on Earth to get a better feel for the terrain.
The Michelin map of France has excellent detail for the whole country, and even though you will be driving alone, I think it would be easier to fold it to show the area and lay it on the seat next to you to check from time to time, than using some electronic device. I think you can get the bigger picture that way.
One more tip. I'm sure you are researching the area and are aware that entrance to Font-de-Gaume is severely limited to avoid damaging the cave and the paintings. What may not be obvious is that you can carry nothing into the cave. No purse, no pack, no camera, nothing. There is a niche next door to the entrance where your stuff, if you have any, will be safely stored behind a locked gate.