There are many options to get to/around Decatur/Atlanta!
First, you can take Marta from the Airport. It’s $1.75 per trip, and you may need to purchase a $0.50 reusable ticket, but you can reload the ticket as much as you want!
You could also take a taxi, but that comes with the taxi price. Also, during heavy traffic, Marta may actually be faster.

Taxi!
To get to Decatur, take the train north (any of the trains will do, as the airport is the southernmost terminus of the Marta line.) Then, at 5 Points station, the N-S and E-W lines meet. Take an east-bound train to E6, Decatur station.

Decatur Station! If you exit on this side, the plaza is directly behind and above you.
Head out of the station (either side) and look around. If you’re by a bus transfer point, head right and go back around the outside of the Marta station. If you’re in a plaza, also head right and back around the ourside of the Marta station. This will bring you to the Decatur square. Turn away from the row of tasty restaurants and toward the old Courthouse, to Ponce de Leon Ave. From there, you should turn left and go to the pedestrian crossing at the T, in front of the statues on benches.

The couple(s) on the bench
Cross the street, and there’s the Holiday Inn! Alternatively, you could call the Holiday Inn and have them pick you up from the station.
Should you want to go out for the day, but your destination isn’t easily accessible by Marta or within 5 miles, and you don’t want to rent a car and pay the $7/day parking fee at the hotel, you could rent a Zip Car. There are many stations in Decatur, the closest being right outside the Holiday Inn doors! You can schedule an hourly rental online.

One of the many Zip Car stations in Decatur
But remember, no matter which method you choose, you cannot park your wagon or buggy around the square.

Nice illustration! Makes me want to use public transportation.