I used to live in that neighborhood. Although it's changed since I was there, I think Salpicon is an excellent suggestion for upscale Mexican. Adobo Grill is right next to Second City, and it's not bad, but Salpicon is better IMHO.
For other cuisines, Bistrot Margot is reasonably good for French bistro fare - probably the best French Bistro within walking distance of Second City. Old Jerusalem has great, cheap, middle eastern food (BYOB), but I think if it were up to me, I'd go to Trattoria Roma - possibly one of the city's longest-running sources for true Italian-style pizza, as well as lots of other Italian specialties.
Bistrot Margot
1437 N. Wells St., Chicago
Old Jerusalem
1411 N. Wells St., Chicago
Trattoria Roma
1535 N. Wells St., Chicago
And of course you can't forget:
Twin Anchors
1655 N. Sedgwick St., Chicago
for the ribs that everyone on LTH reveres.