I want to thank Toritoribe and mdchachi for suggesting I translate 'hang out' into Japanese as 遊ぶ . But I would add these ideas:
Children play.
Teenagers do not play, they hang out.
Adults do not play, they hang out.
When I was teaching English in Japan, it was common for my adult students to say, "I play on the weekend." But I think that by simply telling them, "Adults do not play, they hang out" would have solved the problem.
(I would also add, "I like to go out and have some fun," and "I like to go out and do things for fun,"as alternatives.)