I don't recommend going to the top (89th floor, there isn't a 101st floor) but I'd be a jerk for not recommending going to see the building itself. It was the world's tallest building at one time, after all. The sheer magnitude is impressive to say the least. Skip the 101 mall but take the elevated walkway back to the thoroughly modern and upscale shopping district to see how the better-half lives in Taipei. Treat yourself to a quick walk through of the luxurious Bella Vita Mall if you want to see the "gift-mall" the richest man in Taiwan gave to his daughter.
Xinyi District, Taipei City, Taiwan 110