How about Smith Mountain Lake in VA?
Here's a link to some info about it:
Smith Mountain Lake: Jewel of the Blue Ridge Mountains (This site may be a bit outdated as far as links and such go but its good for some basic info).
You can also do a quick google/wikipedia search for information.
I know you said mountain vacation so you're wondering why I posted a lake website (LOL) but the lake is actually surrounded by mountains:
The lake is connected to Smith Mountain Lake State park which is supposed to be good for all kinds of outdoors activities from water activities to hiking and camping.
Its also very close to the BlueRidge Parkway which is good for scenic drives and hiking, etc. There are quite a few cabins and other lodges to be rented in the area.
Its also within a short drive to the National D-Day Memorial, Hickory Hill Vineyards and Winery, Thomas Jefferson's Poplar Forest, Booker T. Washington National Monument, etc..
The area is convenient to Roanoke, VA and Lynchburg VA so you'll be within range of shopping, dining, etc (though to be honest, the lake area has all of that, but on a smaller scale, of course).
As I mentioned the lake is surrounded by mountains, but there is a section with a sandy beach should you decide to want to take advantage of that option as well..
Location for reference:
My only reservation about suggesting Smith Mountain Lake is that during the summer months the area can get kind of "touristy" but that is only concentrated in one relatively small area of the lake, and, because you are looking for more of a mountain escape, you would probably not have to worry about that too much.