There are several problems with sending a Shuttle to the Moon. Most significantly, when the Shuttle reaches orbit, it has no fuel to thrust its way out of low Earth orbit. Thus, you would need another, separate booster, fully fueled, in orbit already to strap on to the Shuttle.
I assume that you would want to make this a round-trip. That brings up your next problem -- even if you simply looped around the Moon (the lowest fuel-cost option), you would need to re-enter Earth's atmosphere to slow yourself down on the way back. Although hypersonic re-entry flight with the Shuttle has been demonstrated from low Earth orbit, coming back from the Moon, you are traveling half-again as fast as in low Earth orbit. It's not clear that the Shuttle could withstand those temperatures on aerocapture.
Best solution? Assemble a Moon craft in orbit, using Shuttle to transport from Earth to orbit -- and no further, as it was always intended to do.