I live just outside of Atlanta (on the west side), and have been to tons of events at Philips Arena (former Thrashers STH) and the dome. My thoughts:
*IF* money is a primary concern for you, I'd recommend riding MARTA, and board the train at H.E. Holmes. It is a bit 'hood, but I've parked there many times and never had a problem. Common sense is the rule, though. After the game, don't go into the parking lot alone, linger around and go with a group. Leaving the game will be a mother, with long lines. If this doesn't bother you, have at it.
*IF* you can stand to part with $20-30, I would highly recommend driving. As stated, there are several official lots and gypsy lots in the area. Use good judgement, though, when it comes to gypsy lots. Arrive EARLY to the dome area and make a lap or two to gauge prices, just a few blocks can make a big difference in the $$$.
As for food, I recommend the CNN Center. It's your basic food court, Chick Fil A, Wendys, pizza joint, etc. Also, there's several beer places that sell big cups of beer reasonable (if beer is your thing). It tends to get crowded, but seating is plentiful. Also, there's a Taco Mac at the CNN Center, but it's a bit small, and seating can be a chore, but the wings are excellent. The CNN Center is a short walk from the Dome.
As for getting into the Dome: **ARRIVE EARLY**! I can't stress this enough. There are surprisingly few entrances into the Dome, and security getting in is WAY over the top and SLOW. If you wait close to game time to go in, you're gonna be screwed.
Let me know if I can be of any help or if you have any questions.