Although the best thing you take home from this trip probably won't be tangible, here are some ideas for things you can make or buy in Japan to remember your time here.
--Bring a camera, sketchbook and pencil, and/or journal to record your time in Japan from your own perspective. Just take care not to spend the whole time capturing images and thoughts; you need to live a little, too!
--E-mail addresses to keep in touch with your host family and friends later
--Crafts you make with your host family and friends
--a nice set of chopsticks to use (and reuse) at home
--Japanese-style pottery, cups, bowls, etc. (we are planning to decorate some pottery in Ikata, by the way!)
--T-shirts and other clothing
--Japanese 100 yen stores (usually Daisō) are full of small and interesting items, making it easy to bring back something for everyone. (However, most merchandise is made in China, so read labels if you are intent on buying something genuinely Japanese.)
--stickers, stationary, keychains, magnets, knick-knacks, candy, magazines
--If you have your heart set on a katana (sword), yukata (summer kimono), kimono, etc., research online to see how expensive the item is, and bring enough money to pay for it.
Last Word: Memories are worth more than things. Achieve a balance, and don't spend all your time worrying about stuff when there are people to meet and things to do!