nikkiu,
You will love the Dordogne. We were seven family members last June, from 9 yrs to 80 yrs. Jolui gives good advice, especially regarding Gites de France. We didn't want to be in a town, so had a large house close to La Roque Gageac. As Jolui says, the area is small enough that, if you have a car, most everything is within a relatively short drive (most no more than an hour, many within 10-20 min.)
Having been to both, seeing Lascaux II and IV is repetitious. I would opt for IV. Also, at Les Eyzies you are right at Font-de-Gaume, to me the premier cave to visit, and the Museum of Prehistory. Start checking the monuments website two months before your stay if you want to get tix for the English language tour of Font-de-Gaume, as there is usually only one a day. And check the site for the museum. We were there on a day it was closed (a Wed.), so didn't get to see it.
No need for two different accomadations. And, like you, we drove from Bordeaux after renting a car there. The drive to the Sarlat/La Roque area takes about 3-4 hours, depending on your choice of A or D roads. We almost always choose the D roads. Living in California, I don't need to experience freeways/autoroutes on my vacation.
In Bordeaux we stayed a tram ride away from the center of town, at the Hotel Saint Louis Beaulieu-Bordeaux. It was formerly an abbey or convent. Rooms were in the 85-95 euro range, with free parking behind a gate. Rooms were modern yet simple...no tv or ac, but with elevators and a good breakfast at 7.50 euro per person. The cafe on site served a good dinner also. The walk to the tram line was one long block, but traffic near the center of town is no fun to drive in and the trams were cheap, clean and efficient.
I can't recall where we ate, alas. To sightsee, the Cite du Vin is terrific, but probably too much on arrival day. Just strolling around the old center and maybe a stop at the cathedral should be enough. Lots of eateries to choose from.
Back to the Dordogne, since we were in a house, we ate breakfast there, set out for sightseeing in the a.m., and had lunch while out and about. One place we loved was Les Courtines, at La Roque Gageac. Sometimes the cafes at museums and castle towns were excellent and reasonably priced. Although we sometimes prepared dinner at the house, we did have a splurge dinner at Le Grand Bleu in Sarlat, near the train station. There are so many delicious places to eat that you will miss out on part of the Dordogne experience if you don't try some of the regional specialties.
Amusez-vous bien!