West 32nd is near Macy's, and Madison Square Garden. The PATH train station is underneath the Garden, and the PATH train goes back and forth to Hoboken and Jersey City. But you should set aside a LOT of time for commuting if you stay in Jersey. Also, the trains don't run that often late at night, and the buses mostly stop around 1AM from Port Authority, which is 8 blocks north of MSG.
You could take cabs back and forth to Jersey, but it is VERY EXPENSIVE. You'll be spending as much per day on cabs as you do for your hotel room. The Holland Tunnel connects to Greenwich Village and the Lincoln Tunnel comes out around 42nd St/Port Authority. The Geo. Washington Bridge connects wayyy uptown, in Washington Heights. (My neck of the woods)
There are lots of hotels around W32nd-W34th (it's only 8-10 blocks south of Times Square if you want to see a Broadway show).
Cabs are easy to hail -- just stand by the curb, and wave at the ones with the light on at the top of the roof. If the top is dark, it's occupied. if the light is only sort of on around the corners, it's Off Duty. But check a map first -- your destination could very well be within walking distance, or an easy ride by subway.
There are tons on online guides and transportation maps avaible, just Google "NYC tourist information", or go to
http://MTA.info for subway, bus & train routes.