Turner Field was built back in the '90s IIRC and they avoided building new parking by keeping the parking lots from the old stadium. They basically built it on the other side of the parking lots from the old one, so that explains the parking situation there to this day.
The Dome had a giant parking deck that I think was shared with the Georgia World Congress Center building I think, along with a bunch of technically subsurface lots that were on the actual ground level but below the nominal city ground level, but uncovered.
The new Suntrust Stadium out in Cobb or whatever they're calling it now was built with I think one dedicated deck and they put in a shitload of mixed use highrises around it, and people that need to park can usually use either that new deck, the parking of a few adjacent corporate campuses, or park at the Galleria across I-285 and take the pedestrian overpass over that they built concurrently with the new stadium. It's actually a pretty nice setup, other than being on I-75 and I-285 and having zero non-road options to get there.