There's a place called Swings N Things
http://www.sntfun.com/ in Olmsted Township that has Go Karts, Laser Tag, Miniature Golf, Paintball, Bumper Boats, Batting Cages, and an Arcade - probably something for everyone in your group.
Wildwater Kingdom waterpark in Aurora, OH -
http://www.wildwaterfun.com/
Great Lakes Science Center in Cleveland
http://www.glsc.org/index.php
The Cleveland Metroparks are beautiful
http://www.clemetparks.com/
The Cleveland Zoo is great:
http://www.clemetzoo.com/
The Aurora Farms Premium Outelets in Aurora if the girls want to go shopping
http://www.premiumoutlets.com/outlets/ou…
About an hour west of Cleveland in Bellevue, OH is Seneca Caverns which is a cool place to explore:
http://www.senecacavernsohio.com/
Check out
http://www.positivelycleveland.com/. They have a huge list of northeast Ohio area festivals and events.
I've lived in a suburb of Cleveland for 8 years.