I feel the best time to visit Goa is December end. Party, booze, girls; you will get them all.
But if you are a guy wanting some me time and parties are a no-go for you, visit it during Monsoon. The weather is great and every tourist place is least crowded. Although, you can't exercise some water sports; however you will have a great time. Happy Traveling.
July to August that's monsoon time if you love rain and lush green surroundings Nov to Feb if you like to party and love cafe and shack hopping as many will be closed during monsoons. Prefer South Goa if you love calm Vacation and Beautiful less crowded beaches and North Goa if you are a party animal and love the Crowd and Vibe.