December to April is high season — the weather is reliably dry and warm (low 80s F / 27 C), the hurricane risk is gone, and prices are at their peak. Old San Juan and the beaches are busy with US winter escapees and the cruise ships are at their thickest. Book hotels well in advance.
May, June, and November are the shoulder months — still good weather, half the crowds, often the best value. The risk of a tropical storm is low but not zero in June and November.
July through October is hurricane season, peaking in September. Most years pass without a serious storm, but if you travel in this window, watch the forecast. Outside of hurricane scares, the weather is hot and humid but the rain comes in short afternoon bursts that are easy to wait out under a colonnade.
The biggest festivals are the Fiestas de la Calle San Sebastián (third week of January — a four-night street party that fills the old city) and the Festival Casals (late February — classical music in venues around the city). The Día de los Reyes (6 January, Three Kings Day) is the most distinctive Puerto Rican holiday and a good time to be in town.