Absolutely leave the airport. That Hilton is a solid choice, IMO, but a couple blocks further from Centennial Park where the aquarium and World of Coke are. Might be an issue if you're visiting in the dead of summer (though cabs are always an option).

If you're looking for an actual art museum, though, you'll want to look further north, near the Arts Center MARTA station where the High Museum is. You could still stay at the Hilton (or Marriott, Hyatt, or Westin next door) and just ride up a few stops from the hotel to the museum.