I’ve just gone through the process of selecting elementary schools for my children. In the end I ended up selecting the Taipei European School.
Local Schools: A nightmare to get your kids into if the school is good, even if it is in your district, as the good schools are over subscribed. It takes many introductions to the principal to get a place if you don’t get a lottery draw. For kids from the US, if you’re not into total immersion, full-on culture shock, then local schools are not the way to go.
TAS: Possible to get into if you are AIT or have 2 US passports. Great infrastructure/hardware but crap software. Everything the other posters have said about the school are correct. Don’t forget the crime (computer room destroyedlast year) and the drugs in the high school. Just like the US public schools, but you get to pay for it.
TES/TBS: Slightly easier to get into if not AIT or have 2 US passports, but now is fully subscribed. Poor facilities for the elementary school, good facilties for the High School. Great teachers. I am very, very impressed with the management of the school and the quality of the teachers. There are the usual wealthy Taiwanese, but also many international families. You also have the French and German departments which adds to the international flavour. The British curriculum will take some getting used to for the younger kids as it seems about a year or two ahead of the US system. Strong family involvement with things like Saturday soccer.