where can I visit in minneapolis in weekends if I don't have a car?

Nathan-

Welcome to Minnesota. There are a lot of things to do downtown. I'm assuming you live in the city. You can always take a bus to the Mall of America for a day of mall walking, and enjoying the indoor amusement park. I'd also recommend visiting Underwater Adventures (It's fantastic). In your neck of the woods you can visit Como Town Zoo.

http://www.minneapolis.org/page/150-things-to-do.jsp

Here's a cool webdsite that lists 150 things to do downtown. Enjoy.

Namaste-Anora

I'll be honest, the public transportation is not that great for a city of that size. But there is still the lightrail and the bus lines, which you could look up on the MetroTransit website. But bikes would definitely work. Try looking up the Greenway. There is a lot to do, though. You could go to the Minneapolis Institute of Arts, the Guthrie theatre, the Walker Art Center (and its Sculpture Garden), the Ordway, Lake Nokomis, Nicolet Mall, etc...