First, welcome to the neighborhood!
There are lots of great options in and around the neighborhood. Recently, somone asked on another food board, what was there good to eat in and around Wrigley for a visitor. I compiled the following list of some good chow worthy place to eat for them:
Upscale Near Wrigley: Erwin, Yoshi's
Upscale not near Wrigley: Avec,Topolobompo, Avenues, Alinea
Upscale Mexican Near Wrigley: Platiyo
Upscale Mexican Away from Wrigley: Topolobompo, Frontera Grill, Chilpancingo
Inexpensive Mexican near Wrigley: Riques, Playa Azul (order seafood only)
Inexpensive Northside Mexican Several Miles From Wrigley: Oaxaquena (hope I spelled that right, Eldon)
Best Thai Near Wrigley: Thai Authentic Cuisine (TAC)
Cuban Near Wrigley: Cafe 27, Ambassador
Decent Northside Barbeque: Hecky's in Evanston, Fat Willie's
Best Barbeque in Chicago (Southside Takeout Only): Barbara Anne's, Lem's, Honey1 (presently closed for relocation)
Good Bar Food Near Wrigley: Irish Oak, Cleary's on Clark, Duke of Perth
Northside Dogs Fairly Close to Wrigley: Weiner's (Burgers, too)Circle, Byrons
Most Unusual Fast Food Somewhat Near Wrigley: Aloha Grill (Hawaiian) at Clark and Wrightwood
Good Breakfast/Sandwiches/Burgers Somewhat Close to Wrigley: Frances
Best Cup of Vienese Coffee and Pastry Near Wrigley: Julius Meinl at Addison and Southport
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In addition to these, there's a really good cheese shop on Broadway between Surf and Oakdale called Pastoral. It's a small place with a great selection of breads, cheese and salume.
Good bread can be had at the Red Hen on Diversey, east of Broadway.
The best of the thin crust pie that you'll find in the neighborhood is at Renaldi's (Broadway between Diversey and Surf)- specify very thin with light cheese. Otherwise, you may find yourself overwhelmed with a knife and fork kind of pie. There are not a lot of great thin pie options in the neighborhood.
You may be pleased to know that, by the looks of things, an Eatzi's is opening in the next few weeks in the mall at Diversey and Clark.