Goa land of beaches, with lot of history is an ideal spot to visit after May scorching heat. Andaman Islands filled with lot of water sports, greenery and beach waters is an ideal spot to visit after September due to heat. Both being lovely beach destinations, are great spots to visit even in summer. My suggestion would be Goa for more beaches and history. Someday you should make a trip to Andaman.
I would prefer Goa as easily accessible, more accommodation options, activities to indulge etc. but if u have already been Goa, try exploring new place.