Reading some of the threads at Forumosa, a number of people seem to say that the standard and style of teaching at most of the schools in Taipei is about the same. It is probably more important to find a good teacher that suits your learning style rather than go to a particular school.

There are a number of private schools in Taipei. TLI is probably the biggest and most well known. Most of them advertise in the China Post (also check the Chinese language school weblinks at Taiwanderful). I suggest that you find the school that has a location and schedule that suits you. Ask them if it is possible to change teachers if you find the teacher doesn't suit you. Also ask about what materials they will use and whether this matches your learning goals.

Good luck!!!