One offbeat place to visit in Goa is the Arambol Sweet Water Lake. A 20 minute walk from the Arambol Beach takes you to this secluded lake. A nice place to visit at the sunset. A small strip of the beach seperates the lake from the sea. A good idea is to visit the place in the afternoon and return back just around sunset since there are changes in tides and that can be risky.
The path from the beach to the lake is deserted in the off seasons.
The lake is safe to dip your feet in, but has a lot of algae.
What is unique is that even though the lake is right beside the beach, it is a sweet water lake. When you visit north Goa, do visit this place for a good experience with both, a beach and a lake around.
Also check out more offbeat places in Goa like the Kesarval Spring.