On a bike you can just go and keep going, you virtually never need to stop. This continuity is important (on many levels) in exercise. You can go almost anywhere in a city on a bike, as long as there are safe (for you) paths to your destination.
You can ride in tight circles at some intersections, while waiting for an opportunity to continue.
On the one hand, you rarely need to use a brake. On the other hand, you should be always prepared to stop completely and get yourself and the bike up on a curb.
You can, and probably should, ride on the left side of the street most of the time during daylight hours. At night, of course, a philosopher discovers different safety principles.
You are in an excellent position and height to see and read people's intent. Reading intent is critical for safety whenever there are cars present. The more you practice reading intent, the better you get at it. It is part of the body's intelligence. People that tend to not read intent, but only follow certain rules which they consider important (like riding on the right and dressing up like peacocks) are sitting ducks who have abrogated their self-responsibility.
You get into a state of physical momentum. This can be inspiring.
Biking on wet surfaces is one of the best training exercises there is for being a good car driver.
Sprinting is occasionally called for.
There is nothing wrong with sometimes using sidewalks.
Bikes evolved in a culture somewhat ignorant of good body principles. It's good to be somewhat upright on a bike, not hunched over. It's also good to have the legs extended. Thus, you want a large frame such that even with the seat lowered, your legs extend a good distance to the pedals.
There should be no sudden surprises while biking, never ride such that you're blind to the near future. On a dark night, you must see the road surface.
There are subconscious programs which can tell you how to negotiate a complex situation without even having to slow down much. You need to learn to trust the body's wisdom.
Most of the time, you can let the Tao kind of carry you.
A natural pattern is to always zigzag or take diagonal paths from one point to another. You're rarely committed to only taking one street out of an intersection.
You notice that many people have very slow reactions. The physics person in me thinks of them as idiots in 4-Space.
Be like a cat on the bike, you are always in control, without ever thinking about being in control.
Ride such that even if a car tried to kill you, it would probably fail. Never let cars approach you from behind, where you may not be reading their intent.