I always take the NEX.
If you are at the Shinjuku Hilton, many of of the NEX trains run all the way to Shinjuku. See the schedule here: http://www.jreast.co.jp/nex/e_TimeTa...2_u/index.html

When you get off the train, head for the West Exit and walk down the long underground walkway to Nishi Shinkuku. (8 min) you will surface near the Shinjuku Sumitomo Bldg and the Keio Plaza Hotel. Hilton is just behind the Sumitomo Bldg which is a tall (61F) silver triangular bldg on the right as you exit the tunnel.

I did this walk along with a few 100,000 others each morining for 2 years.

This map may be of use as well.
http://www.hilton.com/en/hi/hotels/l...tyhocn=TYOHITW

It does indicate that there is a Hilton shuttle stop at Shinjuku station as well or you could hit the taxi stand right out the West exit and maybe get away with nothing more than the 650 yen or so flag drop.

Hope this is helpful.

Schoflyer