The Racetrack is located behind a gate at the side of the Garden, behind the horse statue.
Entering the Racetrack
There are two ways to enter the Racetrack: either with the Racetrack Key or without it.
With the Racetrack Key
To get the Racetrack Key, Lara must find the hidden part of the Attic and perform a time run all the way downstairs to the Cellar. The key is located at the bottom of an aquarium-like pool. After obtaining the key Lara must make her way back to the gate of the Racetrack.
Without the Racetrack Key
It is possible to enter the Racetrack without the Racetrack Key. Take advantage of the cornerbug to get onto the roof of the mansion. From there you can jump on top of the hedge surrounding the Racetrack. Lara will take a lot of damage while doing this, so aim for the highest part of the hedge.
Taking the Quad Bike off the Racetrack
It is indeed possible to take the Quad Bike off from the Racetrack and drive it along the other parts of the manor's Garden. However, so far only the PlayStation players have succeeded in this because they're able to make the Quad Bike run much faster than on the PC version.