On the south coast of Sri Lanka, just past Galle, is Dalawella Beach. A beautiful piece of coastline with swings right on the beach, turtle watching and just general natural beauty.
It's located about 10 minutes from Unawatuna, you can get a tuktuk there for 1-2$ or take the local bus. Try to get off near Dream Cabana, as this is near the rope swing on the palm tree. Note that the swing is not free, it costs around 3$.
On the beach is also Wijaya Rock, another cool spot to sit for sunset. And apparently you can see turtles from the rock - so keep your eyes pealed.