Assuming an hour into the city and an hour back, plus time for immigration and arriving a little early, i could still conceivably have 3 hours in Taipei.
While not alot, I could at least wander around, have some food and see one or two things.
OK, it's time I start looking at maps to get my bearings before inquiring any further. Thanks to both of you, jimbo99 and jpatokal.