Do you mind if I ask how much you're paying per night?
You might want to look into these as well.
NISHI-SHINJUKU HOTEL Very cheap, clean, in room (lan) internet, etc. I have stayed here most in my trips, and they can't be beat for price/what you get. Seemingly about Y2500 cheaper per room type per night on average than The Washington.
Again, without knowing what you're paying, you can even go to Priceline and negotiate a room for about Y10,000 a night at Shinjuku Prince (which can go up to about 250,000 a night otherwise). And that place is awesome
As for the bars... Man, it has been a while. I know I used to frequent "Mother" and Ax-kixk(??? Bar directly on top of Mother) a lot. Traditional metal/rock type bars that some Jrockers are even known to frequent.
shinjuku mother bar - Google Maps
The thing is literally the size of my Bathroom, but it is still pretty awesome, with a cool staff. It was always close to my Hotels, so I would hit them up pretty often
There is also a rock themed bar on the third floor too called Black I think. It was always closed for one reason or another when I went there though, so I've never actually been.
I think there is one down the street too. But I definitely do not remember the exact location of that one.
They were all in kabuki-cho, I know that for sure.