I like the OMNI at CNN Center, which is very close to the aquarium, but it's not on the direct MARTA line from the airport. From parts of the hotel you can view the broadcast areas. There's a tour too, but it needs to be booked in advance and is relatively expensive.

To me, it would be convenient to be able to go to the hotel easily before/after the aquarium visit, so unless flight times are strange or there's a huge difference in hotel prices, I'd stay downtown. IME all of the ATL airport hotels involve some hassle in getting between the hotel and MARTA, although as pointed out above there are a couple that are a bit betterfor this.

Your family might enjoy the Delta flight museum next to the airport, although it's not really easily walkable from either the terminals or airport hotels.