Links to schedules/locations/information for live music outdoors in the Twin Cities this summer. All of these series include some jazz performances.
Cedar Outdoors (Every Thursday from July 2 - August 27 on the patio at the Cedar Cultural Center. Patio opens at 6, music starts at 7.)
Summer at Northrop (noon - 1 pm, Mondays-Thursdays, Northrop Plaza at the U of M)
Minnesota History Center 9 Nights of Music (6:30 pm - 8pm, Tuesdays in July and August, Laura Jane Musser Plaza, Minnesota History Center)
Outdoors at St. Anthony Main (7 pm - 10 pm Fridays and Saturdays, 5 pm - 8pm Sundays, Minneapolis Riverfront District)
Peavey Plaza during Sommerfest (Friday, July 17 - Saturday, August 1; before each concert inside Orchestra Hall and after the Friday and Saturday night concerts)
Music in the Parks - Minneapolis (Over 200 free performances at Bryant Square Park, Father Hennepin Bluffs, Lake Harriet Bandshell, Minnehaha Falls)
Music in the Parks - St. Paul (Free concerts at Rice Park, Como Lakeside Pavilion, Mears Park, and Phalen Park. The schedule also includes Friday and Saturday evening theater-style musicals at Como Lakeside Pavilion in July and August that aren't free. I'll be ignoring those - not because they cost money but because they're musicals.)