Cabo De Rama beach is the southernmost beach of Goa and is rarely visited by anyone except a few locals. So it's recommended for that dip all by yourself, and you could even make a day picnic of it. Once here, Cabo De Rama Fort can be seen upon the hill behind (and you should go and check it out). This South Goa beach is a bit rocky (the rocks appear and disappear with the tide), but still pretty good for a swim. All in all, you will feel like Robinson Crusoe on your own private beach throughout the year. The beach is about 55kms away from the Goa airport.
P.S. Looking to stay a night? The Cape Goa has beautiful, luxurious and oh-so-romantic cottages.