No goa is not a good option to go in june. as the water activities are not active . and the temperature is not suitable. places to visit in june are:
Himachal pradesh like dharamsala, dalhousie ,manali (it wont show btw)
sikkim(it wont snow)
If you are going on a honeymoon, then you can book one of the resorts in South Goa and spend your time in leisure.To get away from the crowd rush you can plan the trip. Goa is quite deserted in the monsoon season. Be prepared with umbrellas and rain covers. There will not be any water sports during this period. You can also try Northern part of India like Rishikesh , Auli Shimla where the monsoon is not yet arrived and you can beat the heat..
If you are a nature lover and love to explore the lush green areas, then you must obviously visit Goa in monsoons. You can visit and explore South Goa n wander all over in the cool breeze along the countryside which u will not be able to do in any other seasons in Goa. Also it's the off season so you can go to the beaches of North Goa which are usually not so crowded and have a really relaxing and 'me time' over there and also it could be a budget trip for you as well. You can get all the water sports activities in monsoon from the Atlantis watersports like river rafting, fly boarding, kayaking, parasailing and so on. You can just go and check their webites and book a exciting pakacge for watersports with some exciting offers from it. Hope so it would be helpfull for you to decide your trip. https://atlantiswatersports.com/monsoon-activities/
Goa would be an amazing place to be in during June, if you are the kind of person who likes to go to places when not many people visit those. Goa would be perfect in June, everything is cheaper, from accomodation to tickets to travelling. Most shacks and activities would be shut, but beaches would be open and will have barely any people, the weather would be pleasant around evening.
Goa is actually the best to visit during mansoons..less tourists and loads of offbeat activities (beaches are strict no no).
there are lots of unexplored beautiful waterfalls in south goa and loads of treaking opportunities