Two of my favorite less expensive places (everything under $20) in southwest Minneapolis (the city, not the suburbs) are Broder's Southside Pasta Bar and Cafe Twenty Eight. The latter has a lot of local organic meats, and a good beer selection (Surlys draft plus many Belgian). Look at
http://www.broders.com/pasta-bar/index.html or
www.cafetwentyeight.com for menus.