Vänern - the biggest freshwater 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 Pizzeria can not really be recommended, but it's cheap and ok food.
STF Vandrarhem Mariestad, Hamngatan 20, +46 501-104 48. Definitely 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 don't stay there, have a look at it!