I live in the Atlanta suburbs and don't think I would recommend a week-long vacation here. There are places to hike scattered around the city, but the best would be in north Georgia, which would be at least a couple of hours drive from the city. Maybe you could stay a couple of days in the city, then drive to the mountains for a couple of days, then tack a couple more city days on at the end. But, compared to the places that I know you regularly hike, this part of the country may be unimpressive.
I have spent only a little time in Austin and San Antonio, but they are pretty close together, maybe you could combine those two and make a decent trip out of it.
DS - Feb 2010
DD - May 2012