Depending on who's in the cast, I'd say Oh! Calcutta! but just as a stagehand. For the OP, Avenue Q is a good choice but I"d advise you to stay away from The 25th Annual Putnam County Spelling Bee.
Phantom. Just a small role in the ensemble. I love the show, I don’t think I’d ever tire of it and the potential long term job security is most appealing.
One guess. I've actually had a dream once that I was a visiting celebrity Billy Flynn and started to up on my lines.
"Noel [Coward] and I were in Paris once. Adjoining rooms, of course. One night, I felt mischievous, so I knocked on Noel's door, and he asked, 'Who is it?' I lowered my voice and said 'Hotel detective. Have you got a gentleman in your room?' He answered, 'Just a minute, I'll ask him.'" (Beatrice Lillie)
Book Of Mormon would be a blast to do 8x a week. Espically if I played Elder McKinley or Elder Cunningham. Price doesn't seem as "fun" of a role if that makes sense. The campiness of some of the humor and dancing is right up my alley in terms of strengths. Also whoever Danny Bernstein plays in Moulin Rouge.
The revival of Once On This Island. I saw it five times, and I can't remember the last time I so badly wished I was part of a particular Broadway production. Also, I'm still waiting for the opportunity to be the first brown haired, bearded, bari-tenor male to play Evita.
I'd play any role in LI'L ABNER, but particularly Marryin' Sam. I don't know of any other show that aims to be both hilarious yet also heart-felt. (No, I am not an actor/singer, nor am I remotely right for the part of Sam.)
I'd like to be a dancer in the 2010 Promises, Promises revival. I saw the choreography number on The Tonys & was blown away. Eventually, I saw the entire musical at the Broadway Theatre & the sneak preview on The Tonys lived up to expectations. (I'd have to put lifts in my wingtips & learn to do a handstand to be cast.) Fun question!