If you want a relaxed trip then any beach in south is good. If you want a happening trip with partying and clubbing then north goa, around Calangute, baga, Anjuna.
Hi Nirmal,
If you want some peace and quiet then South Goa beaches and if you want great parties and cruises then North Goa. You can probably split the days and experience both.
Here you will find everything you need to plan a trip to Goa - https://www.tripoto.com/goa
Hope this helps.