This is the shop I can really recommend:
Sakuraya or Watch
Kan. Seiya-san is a regular customer here and seems to know all the sales staff.
While I was ogling the Grand Seiko, he found a nice Mission Antarctica on a
Nylon strap.Other shops - except the luxurious shops and department shops at
Ginza - also offer similar discounts, but this shop has in addition a "point
back" system where 1 point equals 1 Yen. You get 10% of your purchase of any
watch - also the already heavily discounted ones - credited to a plastic point
back card. You can then use those points for your next purchase. If you buy
something more expensive then your point balance, you will get additional points
credited for the remaining value.
On the fassade you can see the shop's directory, thus you will already know where to go before you enter the shop. But to be honest, there are so many neon ad's in Shinjuku, it is a pure visual information overkill, quite unbelievable how many shops and shoppers there are in this part of Tokyo.
You go to either Shinjuku or Shinjuku-sanchome station on the Marunochi metro line (red line). If you come from Ginza, then you interchange from the yellow Ginza line at Asakasa-mitsuke (just cross the platform) to the Maronuchi line. And it general the metro works like in e.g. in London, you just check the end station before you get into a train and then most likely you will be OK. I have noticed that since my last visit to Tokyo 4 years ago quite an number of plates, signs and maps have changed to bilingual Japanese/English now.