Great shopping and dining is available in Linden Hills neighborhood of Minneapolis (http://www.linden-hills.com/).
Depends on what you mean by "local market." The Midtown Global Market is awesome, especially during lunchtime or on a weekend. http://www.midtownglobalmarket.org/
Lots of great farmer's markets in the summer!
Minneapolis Farmer's Market on Lyndale Ave and Cesar Chavez Ave or Nicollet Mall
Mill City Farmer's Market on Chicago Ave and 2nd St. S
Also the St. Paul Farmer's Market is supposed to be good -- 5th St. E and Broadway
Here's a list of coops in Twincy: http://twincitiesfood.coop/locations/
Hit one of those if the farmer's markets aren't yet running, or if you're shopping on a weekday..