We had lunch at a little restaurant and bar that claims to be the inventor of the Pina Colada, and it was very good, the food, too! Can't remember the name, but anyone in town can tell you where it was. It's in the shopping district.
If your looking for a true Puerto Rican experience, try EL Jibarito, (not far from the Hotel EL Convento on 100 Cristo St, Old San Juan)and the fort. We ate their 2x when we were in San Juan two years ago. You can't beat the px, less than $20.00 for 2 of us.
The resturant is not much for looks, but boy does the food make up for it. The waitstaff is eagar to assist with recommendations. We had the specials of the day, and one was the Xmas plate (we were there in mid December). And don't forget dessert, home made ice cream. While we were dining several of the hotel staff were there picking up their take out lunch.