Beijing is huge and very spread out, much like most North American cities. Getting from point A to point B isn’t always easy: it’s hot and the streets are jam-packed.
Taxis are cheap and relatively straightforward if you don’t mind the driver smoking in the car and if you can speak Mandarin because there is no chance he will speak English. You used to be able to flag them just about anywhere, but I find they are harder to find now: the parking and pick up/drop off rules are tougher than before. Besides, you can get stuck in traffic, as happened to us on the way from the airport to the hotel.
The subway system is fast, reliable and cheap (tickets are only two yuan), although carts can be very crowded and there are few escalators so we had to carry the stroller up and down the stairs (yay, biceps workout!). Stops are announced in both Mandarin and English (probably a legacy of the 2008 Olympic Games) and trains are very clean compared to, let’s say, Paris.
Although I love riding bicycles, I wouldn’t try it in Beijing—being a pedestrian is challenging enough! Crossing streets invariably involves running across as cars typically speed up when they see people and red lights are just a suggestion to stop. I noticed not that many people bike anymore, people seem to like motorbikes best (and yes, they do ride on the sidewalk if they feel like it).