(photo from Cafe Quasta website)
Cafe Quasta is a board game cafe in the Chuo ward of Niigata City, which serves drinks and has an impressive collection of board and card games. Like a karaoke box, you pay by the amount of time you spend there, during which you can try out any of the games there (or bring your own from home). All of the cafe's games are well organized and in perfect condition, and if you have any questions the owner is happy to explain the rules and walk you through a few rounds.
Drinks must be purchased at the cafe, but you're free to bring your own food and snacks. Cafe Quasta is closed on Tuesdays and Wednesdays, open from 3:00pm to 9:00pm on weekdays, and from 1:00pm to 9:00pm on weekends. Weekdays prices are from 300 yen (1 hour) to 1400 yen (all day), and weekends start at 400 yen (1 hour) to 2200 yen (all day).
The cafe has a really friendly and relaxing atmosphere, and I definitely recommend it for a rainy (or hot summer) day.
Cafe Quasta website: http://quasta.jp/