While the city has an airport, it is not used for commercial flights.
Karlstad is the closest location with an airport, but it does not have major flight connections.
The closest major airport is Gardermoen in Norway. By using the various train or bus connections provided by airport-related companies to get into Oslo itself, it is then possible to switch to the Oslo-Stockholm train that runs past Arvika.
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.
As of 2011, the festival is no longer arranged.
Visit Hamnfesten, , the major party of the year in Arvika. Takes place every summer for three days, usually during the first half of August.
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.
Connected to Arvika stadspark is also Sågudden, a park bordering the local loch, featuring a café, children playgrounds, and
Go swimming at Ingestrand, a popular beach location situated a few minutes outside the city centre.
During winter, skiing is available at the ski slope Rackstadbacken, a ten minute car drive from the city. One lift, few slopes.