Since I have lived in very nearby NJ (~1.2 hrs away) for most of my life, I can count the number of times I've stayed in a hotel in NYC on one hand. So I am not the expert.
There are many choices, including AirBnB (which current Mayor DeBlasio wants to eradicate). Most are quite expensive as land in NYC is dear. But distances are short and transport options abound.
It depends on where you are traveling from, what services and comforts you want on the 11th, and what your timetable might be on the 12th. Also, how much luggage will you be handling and your thoughts about getting to the Manhattan Cruise Terminal.
You don't
have to stay in Midtown Manhattan, as you can get to the MHC in less than an hour from a lot of places in NJ, Westchester and even Brooklyn/Long Island. Of course, if you want to be the NY tourist the day before, and even the morning of (which is not a bad idea), location may be crucial.
Most importantly, we are going on a
Disney cruise to Bermuda!! If you seriously want more thoughts on NYC and port logistics, you can PM me. Hope to meet you on-board!
Doug.