The weather looks to be reasonable on Saturday, crappy on Sunday. Here's some outdoor and indoor ideas:
Walk the Sculpture Garden at the Walker Art Center. All kinds of sculpture from traditional to very conceptual/avant-garde, but it's a nice setting near downtown and a great stroll when the sun's out. You might blow about 1.5 hrs here if you are into art, less if you just power-stroll it.
Walk St. Anthony Main and the Stone Arch Bridge area. Nice historical area along the Mississippi. If you're into museums, the Mill City museum is nearby and features exhibits about the flour mills and building of the city. The Nicollet Island Inn, also right there, has a great brunch. Maybe another hour or so of strolling, looking and reading.
Take a ride/stroll down Summit and Grand aves. in St. Paul. Summit has blocks of beautiful old 19th century mansions, and Grand has lots of independent shops and restaurants. Cafe Latte is a great casual place for a meal and some of the best chocolate cake you'll ever eat.
Rent bicycles at Calhoun Cycle and ride the Grand Rounds trails - about 15 miles (perhaps more?) around the chain-of-lakes in Minneapolis, along the Minnehaha creek and then the Mississippi river. Some beautiful parks and neighborhoods. Lack of foliage will make it a little less gorgeous. You can Rollerblade this, too.
If you're gonna be on the 'Strom and want a nice ride, PM me and I can send you a route around Lake Minnetonka which has some pretty neighborhoods and a few twisty areas. It'll be a little chilly!
There's a Georgia O'Keefe exhibit at the Minneapolis Art Institute - you'll probably want to reserve tickets if you want to see it. The rest of the museum is pretty good, too.
The Science Museum in St. Paul is pretty good, has an IMAX, some good interactive exhibits, etc.
There's a Taiko group performing: Mu Daiko. We see them most every year, and if you like percussion it's worth seeing. Loud and dramatic!
If you like music, check out some of the venues well-known for quality acts: The Dakota (jazz), First Avenue (rock), The Cedar Cultural Center (folk, world).
If you're in the downtown area, make reservations at Hell's Kitchen for breakfast. Might even be worth the 60-minute wait if you don't make reservations ('though you can typically get seated faster if you show up before 8am).
Other great restaurants to try:
Cafe Lurcat (upscale, pricey, but incredibly good)
Victor's 1959 Cafe (cuban dive, but the food's good)
Patrick's French Bakery (soups, sandwiches, pastries - very casual)
Christo's (3 locations, greek, very good food)
Chino Latino (loud, crowded in the evenings, but fun and good food)
Oceannaire (very pricey seafood, but excellent)
Yum! (another bakery with soups, salads, etc. - very casual)
Tanpopo (japanese noodle bar in St. Paul)
Punch! (several locations, Neapolitan-style pizza)
Pizza Nea (near St. Anthony Main, also Neapolitan style)
Brasa (south American; tiny so go off-peak)
Crema cafe (meals, but go for ice cream)
Sebastian Joe's (ice cream)
Lucia's (there's both a sit-down restaurant and a counter-service/takeout)
If you register at the StarTribune website, their restaurant critic is pretty good, and I have found his recommendations to be spot-on. They also have a good weekend events section.
Have a great time!
'07 DL650 ABS
'04 Yamaha V-Star 650 Classic Silverado (gone)
'04 Yamaha TTR225
'03 BMW F650GS (wife's)
'92 Honda XR250L
'86 Honda VT500c (gone)