Well you could always just stay in Alpharetta the night of the concert and taxi back and forth from there. Hit up Taco Mac near the venue and drink drink drink. Just make sure you have phone numbers of cab companies handy in case you can't find one after the end of the show.

I am a big beer drinker so if you need recommendations of great places to drink around town, I have plenty. Alpharetta is the suburbs though so I've never spent more time there than I had to. The venue is not in an area you can walk to stuff from, it's set back off the roads. When you go, you'll be going just for the concert and any lurking around the actual venue beforehand. Once the gates open, they do have decent beers on tap there usually. It's a very nice venue.

As for your questions about neighborhoods, yes, there are a lot of Atlanta areas to avoid. Stick to Buckhead or Midtown. Even downtown can be pretty sketchy at night and it really becomes a bit of a ghost town after business hours. I like midtown a lot, it's really grown a ton in recent years. If you have a car, you can stay just about anywhere (north of downtown ONLY) and get around. The Perimeter Mall area is nice and easy to get to and from and Buckhead and Midtown would still work with a car, just watch for big parking fees.