expedia.ca always helps :)
Rockefeller Center is where they put the huge tree. It s a short walk from Central Park down 5th Ave. To get to the Statue of Liberty, you will need to go all the way Downtown then take a ferry over to it.Try http://www.tripadvisor.com to look for hotels in your budget. Hotels on the side streets of the Upper West Side will probably be your best bet.
The link below will be very helpful. These are hotel near Central Park.Good luckNative New Yorker
go to hotels.com