I had a commenter ask about this so I'll go ahead and post it here (comments box deemed the reply "too long"):
The good points about Shi-da are that they do teach you a lot in a very short amount of time, and even though I whine about the daily quizzes when they're happening, I have to admit that they do force you to study and retain information. You learn a dizzying amount of vocabulary and most of it is useful stuff (I'll get to the stuff that is not useful below). If you study and you spend a good amount of time each week talking to people in Chinese, you will retain it. They are also very good at placing students in the right level.
Now for the critiquue. My biggest annoyances with Shi-da are the teaching methods - go-round, say the vocabulary, read the sentence, move on...same for grammar. It's fine for Asian students who have learned this way before but can be a huge challenge for Westerners who aren't used to this sort of methodology (which I'd argue isn't a very good methodology) - I find after many grammar points that I still don't quite 'get it' because one example and a few exercises is simply not enough.
But...you'd be getting the same treatment at NCCU as at Shi-da, though my sister studies at NCCU and her teacher seems to be a little more into Western teaching methods.
I also find that the vocabulary in the Shi-da books is way too formal for everyday use (mostly). They tell you - with a straight face! - that when you meet someone new you should say "Xinghui" (which is so formal as to be laughable), later on they teach you things like 'xi du' ("to consume narcotics") when your average person says 'ke yao' ('to do drugs'). They teach very formal grammar constructions that you'd never find outside a newspaper and they try to make you use the Beijinghua "er" sound, which is just ridiculous in Taiwan. I used a construction I learned in one of my classes ("Na li you _______________ de daoli?" or "What's the sense in _______ing?"). Sasha, who is commenting here, actually snickered at me! Far too formal. They teach that if someone compliments you you should say 'nali nali' when almost nobody in Taiwan really says that - they say 'bu hui'. That's just a few examples of content that I feel is quite divorced from how Chinese is actually spoken.
I also don't like the politics of the place. Shi-da is a deep blue school and teachers do say things like "Women Zhongguoren" ("We Chinese" but not even "Chinese" as in "people of Chinese origin" - they say it as in "People from China") and the emphasis is on Chinese customs, Chinese traditions - things that came from China. It's as if a unique and parallel Taiwanese culture and populace who hasn't had family in China for 400 years doesn't even exist. It really grates, and I find the whole attitude to be extremely elitist.
I don't find the tests to be entirely fair, either, but that's a separate issue that you'll encounter all over Asia, so no sense bothering about it here. It just reinforces my feeling that the Shi-da program doesn't take into account the needs, obstacles and learning styles of Westerners, which biases the higher levels in favor of the Asian foreigners.
I also don't say this to insult my teacher. She's a very nice lady whose politics I happen to disagree with, but she does to a good job so who cares. It's Shi-da I've got the problem with, not her. I have heard on good authority that the director of the MTC doesn't care about whether MTC teachers have training (the "if you can speak Chinese, you can teach it" attitude, which is so wrong), but haven't personally felt this to be an issue, other than the fact that the grammar is not sufficiently reviewed and practiced.
I'm basing most of this on the review of my sister, who studies there. I feel it's fair to do this, because my critique above was based on my personal experiences at Shi-da and nothing more, so why not base an assessment of NCCU on my sister's experiences?
On the upside, they use the same books as Shi-da, so you get the same vocabulary and grammar at about the same rate. She also speaks highly of her teachers there. The one she has now has a very modern approach to teaching, with lots of reinforcement, activities and practice which she changes around so the students don't get bored.
The thing is, when it comes down to it, NCCU isn't really that much better than Shi-da, and if your NT $30k quote is correct, it's also more expensive.
My sister was shunted around to various levels because the classes at the level she was at were full...and she's a study abroad student so she can't just go elsewhere. She complained that it felt as though they cared far less about her level than their own convenience in terms of class numbers, and therefore didn't care if she learned effectively (seeing as they wouldn't/couldn't place her in the right level). She felt that she was expected to learn an impossible number of new characters per day and that, just like at Shi-da, the testing methods weren't geared well to her level.
I can say in Shi-da's defense that they put me exactly where I needed to be.
And a quick word about TLI and NTU -
As for the specific question of said commenter...
I don't think your placement would be any better at Shi-da, as you have to take a written and oral placement test. If you can't read at all, you'll bomb the written and they'll stick you in a lower level class to compensate for it. Tai-da would be about the same.
So basically, if you want to take a group class, no one university is better than the others (though Taida charges the most so I avoid them, because I don't see any added value to make the extra $ worth spending).
With all that in mind, and considering your situation, you ought to look into TLI (Taipei Language Institute). You can get a one-on-one teacher - for the same price you'd get fewer hours, though - and spend a semester getting your writing caught up to your speaking while setting aside time to work on speaking before enrolling at a university, or just continue there and take a group class. If you can find a few foreigners in a similar situation you could even get a class opened just for your group (Shi-da also offers this but with a minimum of five guaranteed students. I think TLI's minimum is three, but I'm not sure).
TLI isn't a university, it's a business, so in general they're more in tune with their customers' needs. They're a lot more efficient and a lot more flexible and accommodating. They're also cheaper. I really liked my teachers there, and hope to ask at least one for a recommendation I apply for graduate school. The front desk was approachable and efficient. Their class options were more tailored to students' needs, though the standard group classes run about NT$25k per semester and are three hours a day compared to Shi-da's two. I can't take them as I don't have three free hours at the same time every day.
As for prices, it goes something like this:
Tai-da - most expensive (though at NT $30k maybe NCCU can compete for that title)
NCCU - if it's NT$30k as you said
Shi-da - NT $21,000 or so per semester
TLI - NT$25,000/semester, but you get five extra hours of classtime per week
My bone with TLI? For any course, if there is a typhoon day the class is cancelled. For a group class this is no big deal. But at TLI, for a one-on-one, if there's a typhoon day your class is also cancelled and there's no make-up and no refund. That one-on-one student loses the money they pre-paid for the class (same deal if you skip due to illness, work or anything else). I can understand in cases of a person having to cancel, but due to a typhoon day? I lost NT$840 worth of classtime for just that reason and you can bet your butt I was annoyed.