I live in Sandusky Ohio and am very familiar with the Islands. I hope this information will help.
http://www.dogfriendly.com/server/tr...t-in-Bay.shtml This should list not only places to stay but out door eating too!
Put-in-Bay (Putinbay) Chamber Guest Policies Page ( this one list Guest policies and if you go down a bit, it list lodging that takes pets too)