I bought season passes as soon as they became available. They had a limit of 250,000 of these season passes and they sold out quickly.
That should give you a rough idea of how popular this place is, and for good reason. If you enjoy aquariums, this place is going to knock your socks off.
They also limit the number of people entering the building for each hour. It takes a reservation to get in, but once in you can stay as long as you like.
Go to the GA Aquarium web site and get a reservation as far in advance as you can. If you can, get an opening time slot. That will give you a couple of hours before the crowds get thick.
As for campgrounds in the Atlanta area - I am not aware of any in-city facilities but Stone Mountain to the East of town and Twin Lakes to the North are a couple of private campground options. The COE have some very nice facilities at Lake Lanier, also North of town. The State has Hard Labor creek campground and golf course East of town (further away than Stone Mtn) just off I-20, really easy access.