In addition to camping, hiking at one of our national parks is a great family past time.  I started walking with my kids when my youngest was just an infant in a stroller (for some bizarre reason, he wasn't colicky when he was outside) and have continued to explore many trails with them.  First, we were just staying local and checking out local parks.  Now that they are getting a bit older, we are planning to going hiking at one of many national parks as much as possible.  


The following is a great website that lists our national parks: www.nps.gov.