I can personally hang out in a science museum for hours, and the one in St. Paul is one of the more adult-friendly ones I've been to. It still has plenty of kid stuff, but it also has interesting stuff if you have a bit longer attention span as well. But then, I love science so that helps.
Downtown is good. There are some decent bars and stuff. A couple of Irish pubs - The Local is a good one, and I've seen Kieran's Irish Pub but I haven't been in it. Brit's Pub is also a good place to go in downtown. For restaurants, I'm not sure what you're interested in, but there are some pretty good ones around depending on what you like. Nicollet Avenue south of downtown is nicknamed "eat street" for all the restaurants along it:
http://wikitravel.org/en/Minneapolis/Eat_Street. That's nowhere near a complete listing though. My personal recommendation is a place only a few blocks from where I live called the Java restaurant at the corner of 28th and Nicollet. If you want good middle eastern food for a reasonable price, it's the place to go. Be forewarned, the restaurant is a bit dumpy inside (but clean) and the service is pretty bad (they only seem to have one person running the show at any given time, so they're very bad at taking away dishes or refilling water). But the food is worth it. Other ones I like are the Evergreen Chinese restaurant in a basement along Nicollet, the Uptown Diner for breakfast and lunch food on Hennepin, and either Pizza Nea or Punch for authentic Italian-style pizza (Pizza Nea is fancier; Punch is very casual). There's a German restaurant called the Black Forest that has really good sausage.
Unfortunately if there's poor weather, there's not terribly much to set the city apart. Or maybe there is but I am not used to it because I don't have much of a standard of comparison. But I'm at a bit of a loss to come up with stuff other than restaurants and coffee shops that is fun for a rainy day. If it's sunny, the chain of lakes (Lake of the Isles, Calhoun, and Harriet) are pretty nice and have walking paths around them, and there's also an old restored streetcar that runs near Lake Harriet. Outdoor events are fun on sunny days in downtown as well, but if it's rainy there probably won't be much happening. The Mall of America is a tourist trap.