Shinbashi is great spot to feel in Japan. It's call salaryman(Japanese business man called salary-man) paradise! There are many inexpensive izakaya(casual Japanese tavern) .
Shinbashi station is one of the big station in Tokyo and it's so hard to find a good place to meet.
I highly recommend for meeting spot it's call "SL hiroba"
SL is the oldest train (Steam Train) and they have SL on the park.
Go to Hibiya or Ginza exit you can find SL hiroba.
You can meet friends in front of SL train across from Yamada electric department.