In regards to hotels in Manhattan, depending on your budget, may I recommend the link below.
http://travel.yahoo.com/p-hotel-19150198…
In regard to the cheapest and fastest way to get from Newark International to Manhattan at 11pm at night, may I recommend taking the commuter train.
From Newark Airport, take the Newark Airtrain monorail to the Newark International Airport train station, where a connection can be made to the NJ Transit.
Take any New York City-bound (eastbound) NJ Transit train from the Newark International Airport train station to Penn Station New York. The one way fare on the NJ Transit from the airport to the City will cost you $15 USD ($30 USD round trip).
The trip from the airport to the City will take about 20 minutes.
I hope this information is very helpful.
Good luck