Motorcycle parking near Herman Zoo

I've been invited to go to the zoo with my family this Sunday, but I'll be on my motorcycle this weekend in Westchase while my car is being fixed. Does anyone know any safe places to park a motorcycle near Herman Park? I don't mind walking for like 30 minutes. Free is preferred of course, but if anyone knows an underground lot or a lot with motorcycle preferred parking $15 or less, that's a good deal IMO.

It's a tiny bike so I'm worried that if I park it at the park it'll get dozed by a suburban or something.