The teaching methods are virtually identical everywhere. Listen and repeat. Make sentences. Practice in pairs. Answer questions. Textbook based, some ancillaries. The usual stuff.
It's easy enough to find a tutor or tutors if you like, for a very reasonable price. The MTC is at a major university in the largest city in Taiwan -- lots of uni students happy to do language exchange or hire out as tutors.
I think you need to think about what you really want out of this experience. If you want straight American teaching methods (don't get me going on what those really are for Chinese language in the US!
), the best place to find those are in the US. If you are going to Taiwan, make the most of what Taiwan has that you don't get in the US -- the environment, the culture, the people. Don't think that the classes are going to be the most valuable or important aspect of your experience. Classes give you somewhere to be every day, a legal basis for being in Taiwan, and some social structure (people who must speak Mandarin to you, presumably, and who will take care to foster your language development) but that is just a springboard. If you have some Chinese already, take advantage of being able to audit classes for free (check if that's still the case, I've been gone for awhile) at NTNU -- just sit in on something you know something about already and experience it in Chinese. Get involved in on-campus activities. Don't just hang out with American or foreign students. Go to church in Chinese if that's something you might do anyway. This is your chance to get out of a classroom experience (since you already have a fair amount of Chinese and should be able to get language from the environment by now to a greater or lesser degree).