Again looking northwest-ish. The right side of the picture shows Taipei Municipal Stadium and a little bit of the airport.
"But wait!" you scream. "Isn't there a mall at the bottom of Taipei 101?" Yes, there is. But like every other mall in the world, you won't really find anything unique or at a good price. So save your money for the night markets, or at least the souvenir shops at attractions, and buy that expensive shirt when you go back home.
The views are amazing, as you can see in the pictures. There are two levels for the observatory - indoors and outdoors - but if the weather is bad you'll probably want to stay inside. You can see the difference in my photos from indoor and outdoor shots - the indoor shots tend to have a blue tint and sometimes reflections from the glass, despite my efforts to avoid it. But the outdoor observatory has a very high concrete wall which makes it difficult to take shots of nearby locations (such as the Memorial Hall).
Taipei 101 is easy to find. Just look for the gigantic building and walk towards it! Actually, Taipei is quite large and spread out. Take the metro to Taipei City Hall Station and exit using the southwestern-most exit. Walk south on the main street two normal-sized blocks and one massive block (past the city hall) and you'll be there. The entrance is towards the southern end of the block. It takes several (15-20) minutes to walk from the station! Admission is $450NT for adults, and it's open from 10AM to 10PM. Note that you will probably have to wait with a timed ticket, especially during tourist season. It might be less crowded in the late afternoons, and you can see day, sunset, and night views on one trip.