You can make washi
Washi is handmade paper and is typically made from the fibers of one of three types of bushes; gampi, mitsumata, or paper mulberry.
Washi is actually amazingly tough, even more so than paper made from normal wood pulp. It's used in a variety of items such as Japanese kites, lamp shades, woodblock prints, and even clothing.
The production of washi is similar to regular paper. It's normally made using very cold water to prevent the bacteria that causes decomposition of the fibers. The branches of one of the bushes, kozo (paper mulberry), are most often used to make washi. After boiling the branches, the bark is stripped off, and then boiled in lye to remove the starch. After that the fibers are bleached then beaten. Wet balls of the pulp are placed into a vat of water and a sticky liquid made from the tororo plant.
The pulp is lifted from the vat using a special screen. The screen is dipped into the water several times until enough of it is spread across the screen to make a sheet of paper. Each sheet is stacked on top of the others to form a thick pile. The tororo liquid has special properties to keep the sheets from sticking together. Each sheet is then separated and spread on a dryer to complete the process.
If you'd like to try your hand at making washi a good place to do so is in Washi-no-Sato (washi village) in Higashichichibu in Saitama. See their English website for information and directions. (http://www.sainokuni-kanko.jp/eng/experience/053.html)
If you want to buy washi products in Tokyo there are many shops selling them. One good place is Isetatsu. They have some beautiful washi, nice papier-mâché articles, furoshiki (large wrapping cloths) that can be tied into handbags, and framed artwork. All would make a nice gift or reminder of Japan. To read more about the area where Isetatsu is located see my article on DeepJapan at: http://www.deepjapan.org/a/2300