I can't think of anything better to do in Goa than to walk along the beach in the morning or evening. We spent hours just walking up and down looking at all the shells, crabs, sand dollars, etc. If you like to do more than just walk, you'll find plenty to do.
Our hotel was right on the Arabian Ocean. Every morning and evening, we would take walks. The beach was clean and, other than wild dogs and occasional sunbathers, was not crowded.
The Arabian Ocean has a strong undertow, so keep that in mind. There are lots of water sports you can take advantage of -- parasailing, speedboats, water scooter bikey-things, etc. Some men were hawking dolphin cruises -- your money back if you don't see any. I don't know how successful these are.