I hope the $ you put up there is US$.
I dunno what lodging you are looking for, and the number of
days.
Food is not cheap, unless you like street food like hot dogs,
and pizza.
The subway is the best mode of transport, taxis are plentiful,
but thats in manhattan.
To save money visiting musuems, and sightsee spots, I recommend
you get the new york city pass, google it. Not all are free, can't
remember, but I think I got into the Museum of natural history
free. Wow, bestest place ever.
Only idiots shop in NYC. Smart people go to the suburban malls
like Roosevelt mall in garden city. An Abercrombie polo tee will
set you back 60 bucks at its flagship store at fifth avenue. The
same polo tee is retailing 30 bucks at the mall, 10 bucks if they
are clearing.