Geocaching can be super fun. I've never done it on a moped, but I have thought about it.
I lived in Kansas and a nearby small town had some very creative caches. One was one of those tree faces. They'd drilled a nostril and put a tiny canister in there, held up by a magnet. Then they used hot glue to make snot coming out of the nose. You had to yank the snot to find the cache. It was hysterical!
Lots of creatively hidden caches out there. Tons of fun, and great for kids.