The Regency Suites Hotel in midtown Atlanta at 975 West Peachtree Street is one of the closest, if not the closest hotel to a MARTA station. The three-star hotel has free WiFi, family rooms and a fitness center.
Take any red or gold line train to the Midtown MARTA station (including any northbound train from the airport). Take the main exit off the train platform (not to Federal Reserve) and turn left on 10th Street once at street level. The hotel is just a couple doors down.