I work near the airport and last summer scoped out many of the al fresco-ish options, but there may be a few I'm missing. Here are the ones I know about, more or less clockwise from due north.
Sea Salt, Minnehaha - state park
Famous Dave's, 7th St. Paul - screened porch
Champp's, 7th St. Paul - patio
Chevy's, MOA - patio
Au Bon Pain Lyndale near 86th - patio
Potbelly's and Chipotle Lyndale at 494 - patio
Hot Plate and Firefly, Bloomington at 52nd - sidewalk/patio
Fat Lorenzo's, Cedar Ave at Nokomis - sidewalk
5-8, Cedar Ave at the Crosstown - screened deck
It seems like there could be more than this. Because of time constraints, I don't want to venture west of Lyndale, or too much north of the crosstown (7th in St Paul excepted) or east of the river. As it is, Sea Salt is a rare occasion because it is so far and takes so long.
Some of these aren't very chowish - Chevy's for example.