In November the north-east monsoon usually continues through, with most of Sri Lanka seeing some rain and wind. This monsoon is generally heavier than the monsoon earlier in the year, however it is unpredictable and changes year on year, with nice weather breaking through at times and cyclones at others.
Some beach time is possible. The southern and western coasts generally see less rain than the rest of the country in November, and towards the end of the month, there is usually a significant improvement in the weather throughout. You could get some wonderful sunny days on the beach, but if you're looking for guaranteed sun, this is not the time to go. Heading to areas such as Galle where there is more than a beach to explore is a good idea.