Public transportation within Värmland is available, although can be infrequent. The website for Värmlandstrafik is really only in Swedish but is largely usable to English speakers and provides a phone number which you can call to find out more. 
Visit Arvikafestivalen, , one of the major Swedish music festivals. It takes place every summer for three days. The music tends towards various electronic styles, independent or metal, but they have other types of music as well.
If that sounds too noisy for you, walk around in Arvika stadspark instead. It is a lovely park with a small lake and a fountain.