Goa has got lots of gems..I won't call them unexplored, as what I feel is now every place has been touched by mankind.
But yet there are lots of offbeat destinations: There are lots of beautiful waterfall near netravali wildlife sanctuary, you can explore these place.
Also you can visit the tabshikar spice plantation which is unlike the touristy ones(tropical and sahakari), they also organise trekking to nearby waterfall and accommodation options are also there in treehouses and mudhuts. Apart from that you can explore some of the beautiful forts in South goa like Cabo de Rama fort that offers splendid view. explore some of the beaches down far South like- patnem beach and galjibag beach. these are some of the secluded beach and you won't find much crowd there. Near Panjim you can visit fontainhas area for Instagram worthy pics and also visit the Mario Miranda art gallery, they have nice collection of art works on showcase as well as to purchase.
You can also take some bicycle your in old Goa and visit some of the places, b-live is one such agency that organises these activities. ping me if you want to know more about some unique offbeat options in Goa. happy Travelling!!