Gotanda is one or two stops from Shinagawa on the Yamanote line. The pink town is small, but it is also a much quieter scene than Kabukicho or Shibuya. It's on the same side of the station as the Wendy's abd Mos Burger, etc. The last time I was actually in the area myself was probably eight years ago, and as I said, they seemed not to be gaijin friendly. A lot has changed in Japan since those days, howeve, and it might not be as big a deal now. Don't know about prices, but you're unlikely to find many deals for 3000 yen anywhere.
As for meeting non-pros, Roppongi is still the best place to go, and it's not so far from Shinagawa. I'm not exaggerating, most if not all of the Japanese girls who hang out there are there to meet foreign guys, especially on weekends. Also, mosts can speak at least some English. One word of warning about Roppongi, though. Recently there have been a number of dangerous scams against foreign men. Beware of non-Japanese women in Roppongi. Many are very cool, but many are hostesses, strippers, hookers, and worse. I know of three people who have met one of these women, accompanied her from one bar to another, and woken up the next morning without a yen in their pockets, several hundred two several thousand dollars of charges on their cards, and without a clue what happened. I suspect Rohypnol or some other such drug. These problems seem to be located mostly on the side of the street with Don Quijote, etc. In particular it has happened at 911, Wall Street, and a strip club near GasPanic Pizza. Credit card fraud is on the rise in this area as well. Don't use plastic in Roppongi. A friend of mine recently purchased some nice things from Vuitton without even realizing it.