Most popular? That’s tough. Trinidad is truly a gem for local cuisine.
For breakfast, I’d recommend doubles. Have a local take you to a good doubles man during morning rush hour. Try all the toppings. You should be able to put down 2-3, or maybe more if you’re starving. There is a doubles stand at Piarco airport, but it’s not very good.
A close breakfast second is bake and salt fish. Also a delight, but you need to go to a place with a counter. I’d recommend Pancho’s Snackette in town. They were written up in the New York Times: http://www.nytimes.com/2013/03/31/magazine/trinidads-chinese-fusion-cuisine.html
Lunch and dinner are hard to get wrong. Roti is a staple, and the Chinese food is a world away from what you get in America. If you get bake and shark, go to Richard’s in Maracas Bay. Accept no substitutes. Speaking of Maracas, there is an awesome lookout point and snack stand on the way into Maracas. Definitely stop and get pepper mango and whatever else looks good to you.
Seriously, it’s hard to go wrong. Just don’t drink the water. :)