There's 2nd Avenue Corner Pocket and Fat Wally's - both close to the downtown area. Not much happening at FW's but it's a nice room full of Olhausen tables. Corner Pocket has weekly tournaments on Friday nights (8 ball, I believe) and Sunday afternoon (2pm 9ball and 7ish 8ball). They have several bar boxes and a few 9 footers.
There are some pretty good players here in CR, but these are cheap buy-in tourneys so they're mostly just for fun. You might find someone willing to gamble, though.