hospitality

what gift should i give host family for letting me stay as an exchange program from america

It's the thought that counts. Anything large or expensive is likely to cause embarassment or distress.

Mementos of your home town or region make especially good gifts, especially edible ones. Any locally-produced food products seem to go over universally well. Even if the items themselves don't suit Japanese taste, your host family will enjoy trying them. Keychains, t-shirts, small flags, etc. also go over well, especially with younger family members.

If you would like to make a gift to your whole family that will double as a conversation piece, consider investing in a nice (but not-too-large) photobook of your region.