My suggestion was going to be taking it to the school. Since it's class of 2010, this person should still be a student there this year. Just drop it off at the office and let them know it belongs to "Jim Bob Surfer". I'm sure they'd return it or call the student down to the office to retreive it.
Good idea - I think maybe some people are suspicious of a stranger calling up and offering to return a ring. They might be afraid that they'll have to pay a reward to get it back, or that's it's some kind of scam.