I just took the family to see the Georgia Aquarium the 2 weeks ago. Unfortunately, due to our schedule, we had no choice but to go on a Saturday. So we went as early as we could. I was still surprised at just how crowded that place gets. It was wall to wall people.
I would suggest that you go early on a weekday if you want the best chance at smaller crowds. And another thing, order your tickets online well BEFORE you get there. The lines for purchasing your tickets at the Aquarium were very long. It saved us a bit of time waiting in queues by ordering them. Plus we were sure we had tickets for the early morning time slot. Otherwise, if you wait, they may be sold out of the earliest times and you have to wait until your time slot.
I will say that while the Georgia Aquarium was nice and had some interesting things to see. (The Beluga whales were very "frisky" with each other while we were there.

) But personally, I prefer the Chattanooga Aquarium. It was much less crowded, even on a weekend and laid out a little better. But that is just my opinion. (Note that the Chattanooga Aquarium is a fresh water aquarium.)