To get to the Hilton in Shinjuku, take either the Narita Express or the Limousine bus.
I prefer to take the bus after a long flight, as it drops me with my luggage at the hotel's doorstep. The seating, while not generous in pitch, certainly beats having to share legroom with the facing seat's occupant in regular NEX cars (green cars are vastly more comfortable).
If you don't have much luggage, print out the schedules for both, and take whichever leaves first. It will most likely get there first as well, except at rush hour for the bus:
http://www.jreast.co.jp/nex/e_TimeTa...2_u/index.html
http://www.limousinebus.co.jp/e/time...hinjuku_h.html
Getting to the Hilton from the Shinkuju NEX platform is a 15-20 minute walk if you know your way, a little less if the Hilton's shuttle happens to drive by.