As you probably guessed, there's a mall around the base of the tower. I like how an edge of the 101 can be seen in the corner of this building. You can see it through the skylights too, but not in this photo.
There are two high-speed elevators that whiz you to the top in about half a minute. 1,010 meters per minute, or about 37.7 mph. It's so fast, you don't get any sense of the height of the building. They were the fastest in the world for 12 years.
Taipei 101 is on the southeast side of the city. Looking north you can see the Taipei Dome, Songshan airport (not the larger Taoyuan International airport which is much farther west), and in the distance, the mountains of Yangmingshan National Park.
As I mentioned before, the design of the building, not just its height, is what sets it apart. It's rare to have so much ornate decoration on a skyscraper. There are exceptions, of course -- the Petronas Towers in Malaysia being another example.
I visited twice to get the photos you're eyeballing, and both times it was quite busy. However, it wasn't difficult to get to the window you want. There are limits to how many people they'll let up at once, and you can buy tickets for a specific time if you want.
Though I've presented the photos above as if it were one day, I actually came back a week later to get the night photos. I'm glad I did, because the 91st floor wasn't open on my first visit, but it was partially open on my second. Score!
There's oddly less of a vertigo feeling up here, as just beyond the safety fence is a flat surface that extends out several feet/meters. So you can't look almost straight down like you can on the 89th floor.
To get the best view of Taipei 101, you need to hike up Xiangshan, aka Elephant Mountain. I'll warn you, there are a ton of stairs and if you're an idiot like me and go in August, it's also oppressively hot and humid.