You can visit this museum called Ancestral Goa museum at Loutolim to know a lot about the Goan culture and asense of old goa.
Try to explore inner parts of Chapora to try Goan cuisines.
Visit Goa during the christmas, stay with a Goan christian family from a week before.
Goan’s are usually very happy go lucky and friendly people. http://www.ancestralgoa.com