You might read the following article and say, "wait a second, this is exactly like the Sloan Park article!" And you'd be right! It's not laziness so much as this area of Mesa isn't so great for unique restaurants, so like Sloan Park, you'd be better off going to Tempe.
Let's pretend you don't want Chili's. Hohokam Stadium isn't in a great location for local restaurants, but the good thing for you, out of towner, is that Hohokam Stadium is relatively close to ASU, which means it's closer to a little more interesting food.
NOTE - Anything close to ASU will have terrible parking, so plan accordingly. Don't say I didn't warn you.
I'm Want a Hot Dog
Dave's Dog House - My go-to lunch place near the end of my Sun Devil experience, they have great hot dogs in the New England Style, or you can get some crazy toppings like the Mac n Cheese dog (it's a hot dog with mac n cheese and bacon piled on top). You have to actually go on campus to eat there, though, so try not to be a creeper.
Ted's Hot Dogs - Another classic ASU lunch place, but off campus so you won't feel too out of place. Ted's is actually a Buffalo, New York area chain that randomly set up shop in Tempe. I'm assuming one of their family members is a Sun Devil, but who cares? Good place to get a dog or two.
I Want a Classic ASU Experience
Chuckbox - I assume you don't want to get smashed on Malibu Coconut rum and run through the various PV dorms, so get a burger at Chuckbox. It is CASH ONLY, but damn if it isn't near the best burger I've ever had at a restaurant. Seriously, this place is too legit to quit. (Don't say I didn't warn you about CASH ONLY, though).
I've Heard About Mill Avenue
Rula Bula Irish Pub - Come get some good Irish grub and have a Guinness or a Snakebite. I don't remember if this place had the whole thing imported from Ireland, walls and all, or if it was just the tables, chairs, and bric-n-brac. Nice place to relax over a beer or two, just hope you don't go on a night there's live musicians.
World of Beer - Just thinking about this makes me thirsty. Dozens of beer types on tap, hundreds in bottle. What more could you want before or after a ballgame?
Curry Corner - Goodyear Ballpark isn't going to be the only place with an Indian food option, not on my watch.
Cornish Pasty Co - If you've never had a pasty, you're in for a treat. If you have had a pasty, well, what are you waiting for?
There's a lot more to be had in the area, so if you got a good pick then sound off in the comments. Yes, this is a very Tempe-centric list, but maybe it's partially why the Cubs moved a little further west.