Hi Sinecure,

Not sure about timings ( Is the JR Ticket office open that late? but if you wanted Ginza you could take the Limosine bus to T-CAT ( Tokyo City air terminal) and a taxi from there.

As to Shinjuku, the Washington hotel is about a 10 minute walk from Shinjuku station ( windows look a little small from the outside when I walked passed it as I was at the Hilton) and is close to Shinjuku city park ( not Shinjuku goyen park which is on the other side of shinjuku station) and the tokyo metropolitan goverment buildings ( 2 free observation decks) with a tourist office on the ground floor.

Walking to Shinjuku in the morning rush hour you will see thousands of workers coming in the opposite direction but area to the west of shinjuku quieten down later on in the evening but if you go out the north/eastern entrances of the station you get into the evening entertainment area of Shinjuku with the Robot Restaurant,the red light area of Kabukicho and the Golden Gai area ( lots of small bars) worth a walk through ( safe with the usual precautions)

Coming back some NEX trains come from Shinjuku and Shinagawa ( lots of Prince hotels close to the station) before coming together at Tokyo station.

Regards

TBS