Hello keryl, and welcome to Forumosa! 
My goal in coming to Taibei was also to learn to converse in Mandarin. So I moved here with a plan to get a job teaching English to pay the bills while studying independently. As steelersman points out, formal course study isn’t necessary for conversational Mandarin, and some courses will have you spending a lot of time learning to write characters.
That said, IMO you won’t REALLY learn spoken Mandarin well unless you are either taking structured classes, or are a very motivated and self-disciplined person. Once you are busy teaching, you’ll easily find excuses not to study, and the Mandarin goal can easily slip down on the list of priorities. In my case, I managed to focus on the goal and kept progressing, so independent study worked pretty well. Your situation might or might not differ.
Note that in the long run you might regret not being able to read and write some Chinese, and that takes even more discipline than learning to speak. Classes can offer the structure for that, and you can still go the extra mile on your own time for the conversational part, with free language exchanges, SO’s and so on.
In the end, it’s up to you which path you take.[/quote]
I second most of what Dragonbones wrote above. Formal structured class is the best way for most people to learn a balance of reading, writing and speaking Chinese. I would say that, in fact most places focus on writing and reading Chinese characters. Speaking has, from my experience, been relegated to a side line for you to work on your own through language exchange partners or every day encounters. I haven’t studied at TLI or NCCU, only at NTU’s ICLP and NTNU’s MTC programs. Neither focused on speaking.
My experience with NTNU was that they didn’t know what to do about students who want to focus on speaking. The MOE gives them their guidelines for how to structure the program. You have to do well on the tests, and homework also, in order to renew your visa every quarter. The tests we took were all 80% reading/writing, 20% listening then choosing the correct response.
My teacher recommended TLI to me if I wanted to improve my spoken Chinese, and my accent. The issue is they can’t provide a student visa.
I found that NTNU wasn’t very helpful as far as improving my spoken. It was beneficial for reading and writing, but I felt my speaking got worse the longer I was there. I’m also afraid that other programs might have similar limitations. Your Chinese will improve in general since you say you have a basic level, but it you won’t be able to focus solely on speaking.