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)
ladakh
coorg,
kodaikanal
sikkim(it wont snow)
Darjeeling
Meghalaya
rishikesh
mussorrie
almora
etc