There's a train that goes into Mariestad, but it is also served by bus; car always works!
The biggest sweetwater lake in Europe, nice boats, and supposedly a lot of Swedish tourists in summer.
Go swimming, rent a bike, or have some other fun. On Saturdays, there's a market at the main square
There's a fine coffeeshop with great blueberry-vanilla sauce cakes, right at the main street. The Pizzaria can not really be recommended, but it's cheap and ok food
Defenitely sleep at the youth hostel. It's cheap, it's fun. And it has a truly nice setting close to the lake. Moreover, it's several great old wooden houses grouped together in a nice courtyard! If you son't stay there, have a look at it!
Youth Hostel Mariestad: http://www.svenskaturistforeningen.se/templates/hostel.aspx?id=1428