This beer hall is really pretty good as far as atmosphere goes, it was designed by a famous Japanese architect. There are mosaics on all the walls of nice paintings and the columns are kind of a industrial-gothic theme. Overall this gives it a warm, but modern feel. It's a nice change from the bright neon of Ginza outside.
Favorite Dish: The beer, of course! If you are wanting dinner, I suggest you go to a more traditional Japanese restaurant since you're in Tokyo. The fare there is pretty non-Japanese and you can find most of this stuff where you're from, most likely.
Last time I was there it cost around $50 US for four beers and some breadsticks. Not the most cost effective thing you can do there, but it's cheaper than buying a suit at Hermes nearby!