X.O.
I'll start with the free things:
Como Zoo in St. Paul - it is a GREAT zoo, considering that it is free. They do accept a good will donation. Try to catch a Sparky the Seal show. Adjacent to the zoo is a great little amusement park called Como Town, and a conservatory, if she is at all into flowers or other plants. Great photo ops around.
Lake Calhoun in Minneapolis - rent a paddle boat, play on the beach & in the water. Maybe ride bikes around. There are TONS of lakes in and around the cities, so there are great places to cool off.
At the Mall of America -
* Underwater World is a fantastic aquarium!
* The Rain Forest Cafe is a fun experience
* Nickelodeon Universe - age-appropriate rides, and some that might get her to be a bit adventuresome
In downtown St. Paul -
* Minnesota Children's Museum
* Science Museum of Minnesota