I mean it all depends on the purpose. if you want to see the place definitely must check south Goa for churches and if you're looking to go on a beach you should look at north goa. some beaches are much less populated than others. Arambol is one beach that i found was really peaceful. another was vagator. this has been my experience from my first visit. hope it helps
When in Goa, do visit the following places:
Go beaching at: Calangute, Ashwem & Arossim, Anjuna, BAGA, Palolem
Learn history at: Fort Aguada, Chapora Fort, Fort Cabo De Rama, Naval Aviation Museum, Reis Magos Fort
Dudhsagar Falls, Amboli Waterfalls, Pandava Caves and Arvalem Waterfall
Pray at: Basilica Of Bom Jesus, Church Of Our Lady Of Immaculate Conception, Mangeshi Temple
Latin Quarter
Paragliding In Arambol
I hope this help you in planning your memorable trip.
Keep tripping!