Depending on the cast, and exactly when you go will really determine how long your time investment is. However, it is likely that you will be in line from at the latest from 7 am to at least one. There is no way to determine good seats from less good seats as they are given out randomly.
To be honest, I would suspect that your short time in NY could be better spent.
You will never find a consensus on what the best 2 or 3 shows to see will be. Every show has people that love it and every show has detractors.
Right now, the three most buzzed about musicals seem to be:
Matilda
Pippin
Motown (a jukebox musical)
While I have noting bad to say about Motown, I'd reccommend the first two.
If we're not having fun, then why are we doing it?
These are DISCUSSION boards, not mutual admiration boards. Discussion only occurs when we are willing to hear what others are thinking, regardless of whether it is alignment to our own thoughts.