Dunwoody, Sandy Springs, Brookhaven, and
Buckhead are your best bets. These areas are the northern middle of the town. Good areas if you don't want to feel too downtown-ish.
Midtown is good for that, if that's what you're looking for. But Midtown always feels a bit cramped to me, but your tastes may vary.
If you want to get out and about a bit, and maybe get some air, and if the weather is cooperating, I would suggest checking out the
Beltline. There's a million people on it all day, walking and riding bikes, young and old. so you'll blend right in. It's probably the safest part of town, really. That, and it's a nice excuse to get out and show off that butt of yours if you want.
Pack some walking or running shoes.
Marietta/Smyrna are good, too, as is
Alpharetta, but they all feel a bit too far from the heart of the city, particularly if you're only staying for a few days (I would say no further than Smyrna).
Decatur is a bit meh to me...feels a bit country-ish, not so much the landscape, but the people.
Bankhead, College Park, East Point...anything South of I-20, I wouldn't recommend. This includes the airport area. If you're flying in, don't bother settling for any hotels around it. Odds are you're hate yourself for doing it.
So, start with that northern middle.
Hope this helps.