Avenue Q for a 13 year old? Are you serious?
I would recommend Hairspray, 42nd Street, Fiddler, or any of the Disney shows.
When I was at Fiddler, my 18 year old sister and I sat in front of a couple with two kids- probably 8 and 12 or so. One of them asked if next time, they could see the puppet show with the Muppets. Yes, he was referring to Ave q. Apparently the word did not get out to these tourists.
"Why do you care what people might say? Why try to fit into their design?" (Side Show)