Generally I would stay in either Buckhead or Midtown. Downtown has a lot more touristy things to do but is not a pleasant area at night. Dunwoody might be a good alternative area for you to stay since you're going to Alpharetta for the concert. It's a nice (but suburban) area and most of the hotels have free parking (which will be hard to find in Buckhead and Midtown)...and you definitely are better off renting a car.