I never quite understand all the attention that's paid to Aramark, Centerplate, and whoever it is serving food these days at Nationals Park. In a rare example of MLB forgoing a few nickels in the interests of a better fan experience, you're allowed to bring your own food into the stadium. Why would anyone buy the overpriced food at the ballpark? Plus, as any economic study (and the front page of the Sunday Post) will tell you, there's very little benefit to local businesses (some studies actually show a net negative impact) from sports stadiums because most fans just go to the game and go straight home.
So save some money, eat better, and do your civic duty for the neighborhood by picking up food on the way to the park and carrying in. Here are my recommendations. There are tons of places to choose from, but these are my personal top choices--all local businesses that give great quality food and service at a fair price. If you're driving in, these are all easy pit stops on the way. If you're taking the Metro, you can get out at Eastern Market or Capitol South, and then grab the Union Station-Navy Yard Circulator bus, which runs past all these places every 10 minutes and takes you right to the stadium for a buck.
Capitol Hill Tandoor & Grill (Indian)
419 8th Street SE
This is my top choice personally. Good, reasonably priced Indian food, easy to carry out and eat in the bowls they give you. They aren't super-slow or anything, but it's a good idea to call 10-15 minutes ahead if you're in a rush. I recommend the malai kofta and paneer makhni entrees, and don't forget the kashmiri naan and vegetable pakora appetizer.
Starfish Cafe (seafood)
539 8th Street, SE
This is more of a sit-down place, but you won't be sorry carrying out a po' boy with fries. They come in shrimp, catfish, oysters, and scallops varieties. This isn't really a budget option, but you'll get your money's worth. Also if you have a minute I recommend a mojito at the bar.
Good Stuff Eatery (burgers)
303 Pennsylvania Ave S.E.
There's a Five Guys right by the park, but for my money Good Stuff beats Five Guys with a stick all day long. The owner is a guy named Spike who went on one of those TV cooking reality shows on cable. All the burgers are great, and I recommend also getting the onion rings and a milkshake (though you'll have to suck down the milkshake on the bus because you can't carry in drinks, though any half-wit ten-year-old could figure out how to sneak in a few beers, not that I'd encourage anyone to defy park policies).
Old Siam (Thai)
406 8th St, SE
Great Thai place. I always get the panang curry or pad see eew (fat noodles), which can all be served with chicken, beef, pork, tofu or seafood, and the blanket shrimp appetizer is perfect picnic type food.
Those are my top carry-out recommendations. If you have time before or after the game for dinner, I can't make this final recommendation highly enough, especially if you have kids:
La Plaza (Mexican and Salvadorean)
629 Pennsylvania Ave SE
Fantastic margaritas, yummy bottomless chips and salsa, and the best damn service you'll get anywhere. The place is run by a great guy named Henry Mendoza, and pretty much everyone I know who's gone there became a regular. You have a lot of choices for Mexican on the Hill, but forget Banana Cafe, Las Placitas, or La Lomita. La Plaza es el mejor.