There are loads of places to play.
For fun, try New Wave on Soi (road) 7, Morning Night/Hillary's on Soi 4, Gullivers on Soi 5 or Country Road in Soi Cowboy. There are many other bars with tables, just take your pick. These are bars with plenty of foot traffic - tourists and girls for rent, mainly.
For more serious places to play; Hillary's on Soi 11, Ball in Hand soi 4, Players and Sports Academy on Sukhumvit. Here you rent tables by the hour, and there will be very good players around.
All these are easily walkable if you can stand the crowds, or a short taxi ride if you can't. Taxis are dirt cheap - just make sure the driver puts the meter on first.
As far as gambling goes, be careful. 100b games are generally fine in the touristy bars, but personally I'd avoid gambling with Thais. They'll gamble on anything and are poor losers - it's just not worth the effort IMO.
I'm sure Cuaba and others will be able to provide you with more up to date info, but feel free to PM me if you need to know anything else.