Elizabeth Bennet loved to walk. Dramatic things always happened to her when out for a walk, like meeting Mr. Darcy soaking wet on Pemberley's grounds. Well, it happened in the movie anyway, and that's the version of Pride and Prejudice Jane is obsessed with. Perhaps she thinks something similarly dramatic will happen to her on her walks.
And it does. She runs into Martin multiple times, and gets invited to his cabin. She eavesdrops on other people, and she almost karate chops Nobley in the neck as well. In Jane Austen novels, things happen on walks, so it's no surprise that walks are happening events in Austenland as well.