How open are current Zen Buddhism masters to teaching westerners? Would it be acceptable to travel to Japan or China and seek out masters of Buddhism to learn from them? Would they accept the opportunity or is it expected of everyone to seek out their own truth on their own?
Thich Nhat Hanh is a world renowned Zen master who has monasteries in France, USA and several other countries. He teaches and ordains students and monks from all cultures and ethnicities. 

His method of teaching is especially suited for the modern age, since Eastern or Western, cultures are increasingly all the same thanks to globalization. 

I believe Western students will benefit most from working with such teachers, who understand both cultures. Firstly, there's no language barrier, secondly, the western manners and habits won't cause offense or impede progress, and thirdly, the teaching is especially suited for the intellectual Westernized person.

I believe Ven. Thich Nhat Hanh to be no less than a living Bodhisattva, a jewel among teachers. He doesn't teach anymore after an illness a couple of years ago, but his Plum Village tradition still carries on along the path he charted.

One could also travel to Japan or China, many do, but finding a good teacher there can be hit or miss without knowledge of the language, culture and traditions. Ultimately though it is not the teacher, but the student who plays the largest role in enlightenment.

There has been no one who has not been enlightened for want of a good teacher. When there is ardent desire to learn the Dharma, the Dharma will seek the seeker out.