The local libraries do in fact have free tickets to tons of stuff. It works just like checking out a book. They have a stash of 5 or 6 of these "ticket" things and you walk up and check it out just like a book. Most of them were admission for 2.
Regular Prices are below, you can save quite a bit
Minnesota Zoo - $16 - The most popular, everyone was out
Como Zoo - its free already but they like donations
Science Museum - $17
Walker Art Center - $10 - its free every Thursday
There were several more museums. I believe they had admission for anything "educational" in the Twin Cities.