To comment on what others have said here:
I have never seen food or drinks being allowed to be brought into the dome for any event including Championship's. That being said, I assume that some people will bring jackets and they have pockets....
I disagree with my friend Santosh.
The Varsity aka world's largest drive in restaurant, is for the most part priced fairly. The food is greasy which it is known for, but tastes great. If you are over near GA Tech / North avenue Marta station a visit to The Varsity is a must. Get your food and find one of the many different TV rooms or not, to enjoy your food. It is likely too far to walk to though.
There are huge grassy areas outside of the dome to eat and play.
CNN Center right next to the dome, is the place to go with many different fast food places. This includes a favorite here in the south, Chick-Fil-A.
If the pre-order lunch is $5.50 for hamburger, chips & soda that is not bad if you are unable to get to the CNN Center. Sodas during a football game at the dome are $4.50 and pizzas $6. I think they are slightly lowering their prices during Championship's.
Dave