Why do we put telescopes in space? The reason is not to get “closer” to the things we are trying to observe!
Although the Earth’s atmosphere extends much further, we generally think of space as starting about 100 km above the Earth’s surface (see here for more details) and that’s a tiny distance compared even with just the distance to our moon (around 380 000 km).
There is quite a very accessible NASA activity that you can download and do at home with a football and some string to put these distances into perspective.
So if telescopes aren’t put into orbit to get “closer”, why do we do it?
The most important reason, for most space telescopes, is that some types of electromagnetic waves cannot reach down to the Earth’s surface because they are absorbed by the atmosphere, as shown in the diagram below.

From the surface of the Earth we are able to look through the atmosphere using both visible light and radio waves but other types of electromagnetic waves are all blocked so some degree.
So if we want to see what the Universe looks like in x-ray, ultraviolet or infra-red light then we need to place our telescope above the Earth’s atmosphere.
Other effects, such as pollution, clouds, aircraft vapour trails and twinkling (due to movement of the atmosphere) are all secondary problems if the “light” you want to use has been absorbed before it reaches the surface of the Earth!
