SavingAdvice.com Blog Free Things To Do in Topeka When you begin planning a vacation or trip of any sort, it is a good idea to have an itinerary in mind. To save money, add some of these free things to do in Topeka to your plans. Lake Shawnee Lake Shawnee is often cited as one of the top tourist destinations in the state of Kansas. Each year, more than 1 million people visit the park for festivals, camping, and other activities. There are a number of trails to hike and gardens to visit as well. Admission to the park is free, however, campsites and other attractions will come at a cost.