I have a motorcycle in Georgia right now. In Tbilisi, that I'd be willing to rent to you for free if you could change the oil for me, and clean and lube the chain / do some basic checkup etc on it. I left it behind when I ran out of money mid trip, and its currently in storage, though I cannot confirm in what condition, as the hotel I originally was storing it at, had to move the bike due to renovations. Its a 2005 suzuki vstrom, DL1000. I know its bigger than you're looking for, but I had a grand time riding it all over Georgia, and the whole way from California there for that matter!
Let me know if you're interested.
PS Any fees they charge to remove the bike from storage I will cover.