Wicked, Wicked, Wicked!! Don't know any teenager that hasn't loved it. Could be done as a day trip if you booked a matinee...8am Ryanair into Gatwick. Gatwick Express into Victoria. Shopping and lunch around Victoria, Wicked matinee, dinner at Il Posto (lovely Italian near the theatre) then Gatwick Express from Victoria back to the airport in time for the 9pm flight.
Billy Elliot is across the road from Wicked and is also good for teenagers..a bit of language but there are kids in it so I wouldn't worry.
Hairspray if you want something central and Legally Blonde opens in December but tickets for that might be hard to come by.
Packages won't tend to have the popular shows, you'll get deals on the shows that aren't selling so well and have been open for ages.