You could start with Fort Aguada in north Goa. There are variety beaches which you can divide for two days. Vagator beach, Anjuna, Baga, butterfly beach, calangute, candolim along with Mangueshi temple, chapora fort, grand island and museum. There are lot of water sports organised prebook them. Nightlife is something to see in these beaches, besides shopping at calangute beach market, Anjuna flea market, night markets at arpora, panjim and Saturday night bazaar. Don’t miss out on tasting sausages, prawn balchao, Goan prawn curry and kingfish curry. From north Goa proceeding to south Goa you have palolem, agonda, galgibaga, dudhsagar falls, chandreshwar temple, cabo de Rama fort, national park and museum to explore. There are lot of adventure sports to engage yourself, along with shopping at Palolem beach market, Gandhi market and Margao market. The distance between north and south Goa is an hour ride. I will share a few unexplored spots see if it will be suitable for your travel. Netravali, carambolim lake, pequeno island, Rivona caves, fort tiracol.
Kindly check the above Tripoto link for more details.