How many miles is space from Earth?
If you want a really smart-aleck answer, the Earth is in space. Space extends infinitely in all directions, it has no center, and no edge.
Seriously, scientists draw the outer reaches of Earth's atmosphere at 600 mi. The ISS, Hubble, and other orbiting structures are significantly above this. Below this height, there is enough air to slow anything passing through -- known as a "decay of orbit."
At 120 mi is where the Aurora Borealis or "Northern Lights" appear. Meteors burn up at 50 mi. The famous "Ozone layer" is at 30 mi. Jetliners typically fly between here and 10 mi, and below 10 is the air we're most familiar with.