The Shinjuku Hilton is one of the better hotels for free shuttle bus service, however, pretty much running every ten minutes until about 9pm. At Shinjuku station, the shuttle leaves from bus stop 21 on the west side of the station. Exit JR via the west exit, go up one flight to the street, exit the station, turn left and walk about 100 yards.

mjm, so you're not entranced with "Hiltopia" under the hotel, eh?
I agree, the immediate vicinity of all the good hotels in nishi-Shinjuku (both Hyatts, Keio Plaza, Hilton) isn't very interesting.