I also decided to start a posting for links to low cost/free things to do in the Cleveland area, mostly for people with kids. Will definitely update with time, trying to put things on that are a little off the beaten path.
Clague Road Park (free)
A fun park in Westlake with a pond (ducks!), trails, etc. Very fun.
Lake Erie Nature & Science Center (free, small donation recommended)
A cool area in Bay Village, not far from the Lake. Has lots of Ohio wildlife, a Bald Eagle, owls, etc.
Olmsted Falls Park
cute fountains, playgroung, picnic tables and lots of shade