I'll buy a Japan Rail Pass, but I didn't understand if I can use it on nearby subway stations such as Ningyocho, Kodenmacho and others. Is it possible?
No. These are part of the Tokyo Metro, which is not operated by JR, and thus the JR pass is not valid there.
The nearest JR station is Shin-Nihombashi on the Sōbu line, but it's a commuter line that goes only one stop into Tokyo to Toyko main station, where you could change to urban Chūō or Yamanote lines. The Yamanote line itself has the Kanda station a bit further, but that's already a significant walking distance.
is it possible to visit typical tourist places in Tokyo using the JR Pass?
There are some JR lines that are useful within Tokyo, namely the Yamanote and Chūō, and together they cover many of the main tourist attractions, at least if you're prepared to walk a bit. But you'll often take a lot longer than if you were willing to freely use all public transportation via the Suica card.
Another factor is that with the JR pass, you cannot use the normal entry/exit gates - you have to find one where there's a JR employee and show it to them (or climb over the gates and look like a criminal).
So basically, relying only on a JR pass within Tokyo is possible but very inconvenient. Of course you can still use it to save some money when there's a good connection to your target through a JR line, but that would be the case far more often if you chose a hotel near a JR station.