You are correct about green tea, buuuuuuuuuuut:
there's wheat tea, barley tea, soba tea, black bean tea, yuzu tea, a coca cola product called Sokenbicha which is wheat/barley/random other herbs that you can get almost everywhere.
You can always ask for just plain ole water too. Ice or hot.

If you want food so good it makes me consider being vegan, go here:
http://eng.shukubo.net/vegetarian-cooking.html