For an observatory that monitors trajectories of objects in the solar system, you want these features:
No atmosphere. Atmospheres do horrible stuff to light that needs to be corrected for. Removing scattering gases and dust from the light path makes the telescope much, much less complex to build for the same resulting image quality.
Ability to frequently scan the sky. If you observe an object once, you only have its direction from a single point in space. That's not even enough to deduce how far it is away. To accurately measure its trajectory, you need many observations to see how the object moves over time.
Observations from different locations. While not exactly required, this helps in determining how far an object is away.
Since Venus and Earth have dense atmospheres, they are out of the race. Mars has an atmosphere, but it is thin. So, an observatory on Mars would make some sense if you already have a base on Mars (= cheaper to build where you have materials and workers available).
Jupiter, Saturn, Uranus and Neptune are gas planets, so they are out of the race as well.
Pluto is a nice, dark place with a very thin atmosphere, but it's very far out. As such, it'll have a hard time detecting stuff that's within the inner system: The sun will tend to blind it, the objects on the far side of the sun will be very far away, and the object on the near side will be only thin crescents. Not a good place for an observatory.
This leaves Mercury and Luna. Both have the same problem: an extended day-night cycle. A day and night last 28d on Luna, and 176d on Mercury. Both lack an atmosphere, both are fairly central in the solar system. Luna allows for a scan of the sky every 28 days. Due to Mercury's weird rotational period, it allows a scan every 59 days.
However, Luna is much more amenable to human population. Mercury turns freaking hot during the day and the day-night cycle is very long. So cooling a human habitat during the day is a nightmare, and heating the same habitat during the night is also a nightmare due to the lack of energy from sunlight. The temperature swings on the moon are much less of an issue, and the shorter day-night cycle allows for easier storage of enough energy to get over the night.
So, I'd say: The far side of the moon is your best bet.