i agree with what's been said about classical indian music, you either do it seriously or not at all. in any case, you'd have to learn directly from a teacher and that's probably not an option for you. but, you could learn bansuri (bamboo flute) just for your own uses. idk about buddhism, but it certainly has ties to hinduism. beautiful instrument when played well.
from japan, you could learn shakuhachi or shamisen
on the european side, there's folk harp and hammered dulcimer
last year i started playing nay, the reed flute used across the arabic region (or ney in turkey, slightly different instruments). i can't really comment on how effective any published instructional material is, again it's something you typically 'learn by example' from a teacher. you might also have fun with ud, or qanun if you can find one.
or you could learn to overtone sing. won't cost you anything...