Closest Saturday tourney will be at Snookers in Providence RI and that is a qualification event for a bigger tourament later this month at the same location. It is only an hour from Boston and it's the place to go if you want to see some of the better players in the region while you are in the area.
There are tourneys every other Saturday at World Class Billiards in Peabody MA., but I think the next tournament isn't until next weekend.