12 hours should give you enough time to take a train to Tokyo. The big pool halls are CUE in Shibuya and Rosa Kaikan in Ikebukuro. There are also quite a few smaller places around where you would be more likely to find someone to play.
I agree, Cue in Shibuya is a great place. Additionally, you might hit Bagus in Roppongi as it's a little closer to the train station, and you're more likely to find somebody to play. The locals are very shy, and most likely won't approach you for either a 'friendly' or action, but at Bagus you'll most likely either run into other foreigners, or you find somebody that's used to foreigners.