Although technically not out of Japan, Okinawa is very popular in the same way Hawaii is to mainland Americans.
Other than that, “short” trips basically radiate from the country. If you check the routes of some discount airlines (peach, vanilla air, etc), you get an idea of popular destinations: Seoul, Taipei, Hong Kong, etc.
Just like Molly said, the Japanese are always off to Hawaii – they LOVE Hawaii!
I was optimistic about flights being cheap but, not particularly surprisingly considering the distance, they’re not :(
Cheaper, closer places I’ve heard Japanese people talk about holidaying include South Korea, Taiwan and places in South East Asia like Thailand, the Philippines, Malaysia etc! A bit further than a short trip but it’s like 6-8 hours.