Will you be driving or using public transportation? Why did you select that specific area for a week-long stay? Where will you be before you reach that area? Where will you be heading next?
I spent five nights in Bordeaux last summer (late May/early June) and took a day-trip to St.-Emilion by train. However, I had 43 days to spend in western France. I enjoyed Bordeaux; it's a handsome city and I liked the museums. It is not, I would say, one of France's very most engaging destinations for the typical tourist.
St.-Emilion is a very pretty, hilly, historic town. Very touristy at the lower level; less so up at the top of the town. I spent several hours just walking all the streets. I don't care for wine, so I spent no time tasting or shopping. I think a one-day trip would be sufficient for nearly all tourists. If you're looking for a less-busy place to base for a few days, I'm not sure St.-Emilion is the best choice.
With 7 days for that general area, I would spend most of it to the east, in the Dordogne and/or Lot. I had 11 days there and could definitely have spent longer. I didn't have a car, so it was a struggle for me to get to the tiny places that many people speak of; they don't have rail services and sometimes not even bus service. I had to stay in a series of sizable towns in order to have access to the buses I needed to hit a few of the smaller places--and even so I had to do significant rural walking. But my base towns were very attractive. I guess my two favorites were Perigueux and Cahors. I also liked (hilly) Figeac when I day-tripped there.
There are several people on the forum who love the Dordogne and have visited it by car. They can help you with your planning if you intend to rent a vehicle.