While it's true that there's a lack of decent food in the immediate vicinity of Wrigley, you don't have to go far. There are plenty of very-good-to-excellent options within a half mile of Wrigley, mostly on Southport but also on Irving Park. Here's a laundry list in no particular order:
Toons - solid bar food
Tango Sur - Argentine steak, BYOB, often has long waits
Bodega Sur - same owners as Tango Sur, similar food, booze sold onsite
El Mercado - market w/empanadas sold by the register, also same owners as Tango Sur
Coalfire Pizza - fantastic Neopolitan-ish pizza, typically super fast
Panino's Cafe - underrated Neopolitan-style pizza
Cafe Tola - takeaway empanadas, non-traditional but amazing
5411 - empanadas, not nearly as good as Tola or El Mercado but has seating and booze
Tac Quick - excellent Thai
Byron's Hot dogs - solid dog
Sushi Mura - perfectly fine neighborhood sushi joint #1
Rise - perfectly fine neighborhood sushi joint #2
Crosby's Kitchen - well-done family-friendly American fare with full bar
Ella Elli - wine bar owned by same people as Crosby's Kitchen
Corridor Brewery - decent beer, upscale bar food
Jeni's Splended Ice Cream - great ice cream, long waits in the summer
Dairy Queen - because sometimes you just want a Blizzard
A little further but all within about a mile of the park:
Roost Carolina Kitchen - Nashville hot chicken
Cere's Table - upscale Italian
DryHop Brewers - good (mostly hoppy) beer, upscale bar food
Cafe Tola #3 - another outpost of Cafe Tola, just a bit further west on Addison
Cafe Orchid - solid Turkish food, not my favorite but it's gotten some love on the board
Cafe El Tapatio - Mexican
Coda di Volpe - good pastas and pizza
The Spanish Square - tapas
Fahlstrom's Fish Market - great seafood, if a bit inconsistent in my experience
Murphy's Red Hots - for my money one of the best hot dog stands in the city