Trinity has been a Providence staple for many years, and its quality has not deteriorated at all in that time. They still produce award-winning brews on-premises, and they still have the great traditional pub hangout atmosphere.
Come in the heavy oak doors, sit at the bar facing the large beer vats, or ask for seating downstairs in the lounge, which is surrounded by plenty of TVs to watch the game on. Order a pilsner, a RI IPA (the best in the state), or one of the varieties of stouts the brewpub produces. Usually only six varieties of beer are available at a time, but they run such a gamut that no matter when you go, you're bound to find one you love. You can join a Mug Club for a yearly fee which entitles you to some excellent beer benefits.
If you're hungry, Trinity takes "pub grub" to a higher level. The hand-tossed pizzas are fresh, not frozen like most bars, and are produced on real pizza dough and with an assortment of toppings (I recommend the Carnivore pizza - half is guaranteed to fill up a big belly like mine). The chili is awesome, as are the tasty wings.
The only detriment to this place is some of the barstaff, who can occasionally behave like enormous jerks when it's busy. Most of them are good, though, and provide good company if you're by yourself to drink some good beer.