So, there are no direct words to say " hang out ", but there are alternative ways of saying it. 一緒に付き合わない？ 付き合う　is one of the ways of saying it. Now, this can have two situations. The first is when you are asking your same sex friends of going out for dinner, fun and etc. The second one is when you are asking out some one who is not of your sex out, usually for a date. Even if you are not looking to romantically be together, it tends to sound that way when one uses it. どこかへ遊びに行こう。 遊びに行く　is another way of saying it. It directly means " to go and play " but you can use it as hang out. This is something you can use for both sexes without having any awkward situations. This would be the safest way of using it.