LaGrange Points

from the Wikipedia article:

The Lagrange L4 and L5 points have the potential advantage of providing instant parallax for a pair of space telescopes.
Being stable, the L4 and L5 points are relatively easy to get to and cheap (in terms of fuel) to be stationed at.
As a result of being stable, the L4 and L5 points also collect and retain some debris.
There is some debris, including one known asteroid (2010 TK7) but the density of debris is currently unknown. It is slightly difficult to observe any current debris from the Earth since the L4/L5 points tend to be in the daytime sky.
Missions to send probes to L4/L5 have been proposed but not yet organised. Such missions would probably allow us to evaluate the level of threat of collision and allow us to weigh the cost/benefit/risk of deploying a pair of space telescopes.
Instant parallax is useful for observing relatively near objects, but much space telescope interest seems to be concerned with seeing distant objects, for which parallax is too small to be relevant.
The L1 and L2 points, which we are using are unstable, so do not suffer from the debris issue, but have the advantage of low fuel requirement to stay on station.

L3 lies behind the Sun, opposite Earth, just beyond our planet’s orbit. Objects in L3 cannot be seen from Earth. It offers the potential to observe the far side of the Sun. A spacecraft at L1, L2, or L3 is ‘meta-stable’, like a ball sitting on top of a hill.

To be terribly precise, the L2 point is literally a point. It’s like the top of a huge, slippery glass dome. If you are slightly off that point, you will slowly drift away, and more and more quickly away. So, only one satellite can sit on the top.

However, if you settle for being approximately there but not exactly, and have a rocket, then no problem. When the drift becomes too big, just use your rocket to get close enough again. So, the number of satellites that can be close enough to L2 depends on a few different questions including how close you must be, to count yourself among the “close enough”.

https://en.wikipedia.org/wiki/Lagrangian_mechanics

credit to: Taylor Fountain

Objects presently residing at the following regions of space:

Earth-Moon

L1 and L3 – nothing

L2 – Qucqiao (China) https://en.wikipedia.org/wiki/Queqiao-1

Equuleus (Japan) https://en.wikipedia.org/wiki/EQUULEUS

L4 – Kordylewski Clouds https://en.wikipedia.org/wiki/Kordylewski_cloud

Tdrs https://en.wikipedia.org/wiki/TDRS-1

L5 – Kordylewski Clouds https://en.wikipedia.org/wiki/Kordylewski_cloud

L5 Society https://en.wikipedia.org/wiki/L5_Society

Sun-Earth