I am staying in Minneapolis during August. Are there any trips to make from there to diffrent cities/places (maybe chicago, or South Dakota) with a bus or a train since I will not have a car. Any tips on cities/places to visit from there?

Minneapolis has a good light rail system.

You can go to Mall of America, several museums, sporting events.

Minnesota State Fair will be the last part of August, first part of September.

http://www.metrotransit.org/

Amtrak runs out of St. Paul and would get you to Chicago easily or even out to Montana if you have the time. Check their website for schedules/prices. Another option is renting a car and visiting nearby areas. Do you know where in Mpls you will be staying? Light rail is a bit limited, but we have a bus system as well.

I will be staying in Bloomington

I am not staying at a hotel I am staying with my aunt but she does not really like to drive so i can't count on a car

Go south towards Albert Lea and go to the Spam Museum!!