Klarälvsbanan (http://www.klaralvsbanan.se/) is a very good and level bike path to the north from Karlstad, in total 90 kilometers along the Klarälven river. It is a former railway track, so it is car-free. It is also very good for by roller scating.
Local and regional buses are managed by Värmlandstrafik. Schedules and a travel planner is available at their site Kollplatsen (http://www.kollplatsen.co...).