If they're a person who is going for the first time to NY, and loves spectacles; Phantom or Wicked.
If they're civilised, and have seen a musical before I usually recommend a play. Up until recently it was 'The Seagull', now it's 'Equus' and 'Speed the Plow'.
I need to recommend Wicked because even though it is such a tourist show it's still great. And I only see shows before they close so all the ones I would recommend are gone but a few a would have are A Chorus Line, [title of show], and Legally Blonde.
I find myself recommending the 39 steps a lot. Mostly because its a departure from the the big splashy b'way musical, but is still an audience pleaser. I would recommend August much more, but most of the people who ask me what they should see are not that "type" of theatre goer. :)
Fuerzabruta, August: Osage County and Altar Boyz. I haven't been to NYC since Dec. of 2007 so I haven't seen anything that opened this past season. I think August: Osage is a must see and Fuerzabruta and Altar Boyz are a really good time.
I know that many of yall recommended August Osage County, so we'll be seeing that when we come in April! I'm so excited to see it! We began making trips to New York once or twice a year in the summer of 2004, and we've seen so many great musicals and plays. I think I'd recommend Wicked for anyone who is going for the first time because I think it's a wonderful musical! I'd also recommend keeping up on the latest info. That's what we did and we were lucky to see Cyrano and Macbeth which weren't as highly touted to "tourists" as the big musicals.
It totally depends on the person. But right now, the best productions on Broadway are AUGUST, GYPSY, and BILLY ELLIOT.
For tourists though, WICKED is what I tend to recommend although it's obviously hard to get tickets to. Lately I've been recommending IN THE HEIGHTS to out of towners...it's easier to get tickets to and while not as flashy as WICKED, it's still a general crowd-pleaser for nearly every demographic.