You're likely going to be attending the concert at Verizon Wireless Amphitheater at Encore Park.
It's a relatively new (5 years old, maybe?) venue and is gorgeous. I've been to several concerts there. Parking is ample, but tricky. Getting in and out is a little confusing because the amphitheater is in a business park that is busy during the day, but empty at night.
While staying a few days in Downtown Atlanta, there should be plenty to keep you busy. There's the
Georgia Aquarium, the
Coke Museum, the
College Football Hall of Fame, etc. All of this is easily accessible by
MARTA which runs from the airport to downtown, then splits off in a few different directions.
HOWEVER, if it was me, I'd rent a car. Metro Atlanta is huge, and there is a ton of other stuff to see/do that's not within walking distance of MARTA.
If you rent a car, you shouldn't need a hotel in Alpharetta. There's plenty of HGI's, Hamptons, etc. in and around Alpharetta. They should all be around $120/night.
If you don't rent a car, MARTA runs to the North Springs station. However, you'll still need a cab/Uber to get you to the Amphitheater which is 10+ miles away. It could get expensive. Be mindful that MARTA drastically reduces their schedule late at night, so you could be waiting a while for a train, if one comes at all. Again, I'd recommend getting a car. Keep in mind that the theater is 30+ miles from "downtown" and there's no public transportation that will easily get you from one to the other.
MARTA is pretty safe if you remain aware of your surroundings. Don't get on the east/west lines, stick to the north/south lines, especially towards the airport.
Depending on your budget, look for hotels in Midtown or Buckhead. You'll pay a little more, but good restaurants, shops, etc. will be nearby.
Stop at the
Varsity at your own risk. Bring some Tums.
Get a Frozen Orange and an order of onion rings.
Some of my favorite restaurants are
Antico Pizza,
Local Three Kitchen and Bar, and
Holeman and Finch.
TL;DR: Get a rental car. Stay north of I-20. Have a great time!