What to bring your host family? Here are some ideas if you're stuck:
1-Home (something representative of Red Wing, Minnesota, or the US in general)
--T-shirts, jerseys, caps, local products, nice photo books, art
2-Soul (something that reflects your skills or values)
--Your own handmade arts and crafts, tastefully framed, mounted, or wrapped
--Ingredients and a recipe for a dish you can make for the family
--Fair-trade coffee, chocolate, clothing, or other products (*be aware that many people don't own a coffee bean grinder, so pre-ground coffee is a safer option. Also, chocolate will assuredly melt in the summertime.)
--Music CDs, especially if you e-mail with your host family before the trip and learn about an artist or style of music they enjoy
--Most DVDs are region-specific, so American (Region 1) DVDs will not play in a Japanese (Region 2) DVD player and vice versa. (Not recommended.)
--Toys if there are younger children in your host family
--Popular magazines, posters
--Little things like American coins, pens, pencils, stickers, and gum for other people you meet in Ikata
Japanese homes are famously much smaller on average than an American home, so think ahead when you are gift-shopping. An oversize knickknack, even if it's regional or soulful, will probably just collect dust. The vast majority of Japanese gifts are food or drink.
Last word: Whatever you decide on, make sure to put some thought into the gift and wrap it carefully and attractively. When you give a gift to someone, he or she might decide not to open it right away--waiting for a private moment to do so--but this is simply traditional etiquette and not a dismissal of your gift.