I don't believe hotels run shuttles but you would need to check.
Zoo is a couple blocks from not a great area. No mass transit to there except for bus which I do not recommend. Go to zoo, have a good time, and leave that area.
Aquarium is a couple blocks from the rail line (MARTA) and is in a downtown tourist area (keep your head up but nothing to run from during tourist hours).
Look up Atlanta City Pass. You can get discounts for combining various attractions. College Football Hall of Fame, World of Coke, etc.
I suggest staying near the Aquarium and driving car, taxi or Uber to the zoo. You can stay outside city but there won't be much else to do in the burbs unless you have some good intel on the area you are staying.
Fall is my favorite time in ATL. Good weather most of the time. Enjoy your trip.