Air Busan flies from Busan to Fukuoka, Osaka (Kansai) and Tokyo (Narita). I've flown with them before and they were great. You can buy tickets on their English website, and if you buy them far enough in advance you can usually get pretty reasonable prices. They or Jeju Air, mentioned by a previous poster, are probably your best bet for a cheap flight.
The ferry you mention in your post is from Busan to Fukuoka/Hakata. It's called the JR Beetle or MiraeJet in Korea but I don't think it's any cheaper than flying if you book your plane tickets in advance.
There's also a ferry from my city (Donghae) to Sakaiminato in Tottori-ken, Japan. I think it's reasonably priced, but it's slow (usually overnight I think) and Sakaiminato is very far from anywhere in Japan you're likely to want to go.
Here are the websites for Air Busan and Jeju Air:
[http://en.airbusan.com/AB/airbusan/english/main.jsp]
[http://www.jejuair.net/] (there's a link for the English in the top right)