http://centralparkinn.com/index.html
we stayed there...used to be called central park hostel. Double rooms are nice enough and much much cheaper than hotels. As someone said earlier you only sleep there.
Right on the subway too so real handy to get about.
When we were there, a small restaurant is just up from the docks. Served the biggest meat sandwich I've ever had....
NYC is an amazing place and not sure a week is long enough!!