I wouldn't really call it rap. I'm not a rap fan at all either. What Miranda did was take the music he grew up with and merged it what we commonly associate with showtunes, to create an interesting and unique sound.
In an interview he explained:
Tell me about the various styles of music represented:
Oh, it's such a gumbo. I don't think the average theatergoer knows how many different types of Latin music we're representing. They see the broad strokes. They see that Usnavi speaks in hip-hop, and when we hear from the Abuela, we hear Cuban mambo. “Carnaval” is a mix of a Puerto Rican plena and other Mexican types of music; it's like a pan-Latin folk tune. Vanessa sings a Dominican merengue. Every character speaks in their homeland language.
This commercial should give you a good idea:
http://intheheightsthemusical.com/media.html Honestly Lin-Manuel Miranda is a genius, this is truly a great piece of art, and there is so much talent involved (not just the actors, the set is phenomenal) and the songs are quite catchy as well.
I really think you would be doing yourself a disservice to miss this show.
And if you hate it, hey at least now you don't have to wonder what you were missing, but it's hard to imagine anyone hating this show at all.
<-- Gwen Stewart, SOLoist at the last show of RENT
Cages or wings?
Which do you prefer?
Ask the birds.
Fear or love, baby?
Don't say the answer
Actions speak louder than words.
(Tick, Tick... BOOM!)