Originally Posted by rustykettel

The escalator from the lobby will take you down to Hiltopia shopping arcade. Walk through there and take another escalator (maybe it's a stairs down, only escalator back up for that one) down to the underground tunnel. Turn left for Nishi-Shinjuku or right for the Tochomae Station (Toei Oedo).

I'm pretty sure there's a bank of ticket machines in the Nishi-Shinjuku station, but I've always used Suica/Pasmo so never investigated those.

Going back to the hotel, you want exit C8. Out of the ticket gates, veer to the right past the bakery, then turn right to the stairs slightly afterwards. I don't recall any signage for C8/Hilton at the turn and I'm blanking at what the signage is. Go down the stairs and you'll be back in the long tunnel. There is a Hilton sign on the wall at the C8 entrance.

Good luck!^