The fastest way to Put-in-Bay and Kelleys island is by hopping on the Kelleys Island Ferry Boat Line or Jet Express. The round trip fare is around $23. By the way, if you love bird watching you will enjoy Kelleys island as multitudes of migrating birds use this island as a base to cross Lake Erie.
getting to put in bay from cleveland I visited put in bay from cleveland last year by taking the Ohio Route 53 North for the car ferry. For the passenger ferry, you need to take the Ohio Route 2 West to then exit 163 North Port Clinton (I think the company was jet express).
Jet Express operates from Port Clinton and not far from them another operator services the Put-in Bay route which is the Miller boat line. I believe Miller's ferry is cheaper and offers free parking.