Why do radio astronomers place their telescopes in deep valleys? &
Why do optical astronomers place their telescopes on top of mountains?
They don’t. Not always. The VLA – the Very Large Array, in New Mexico is on a flat plain. The new Allen array is on a fairly flat plain as well. Radio telescopes aren’t much bothered by atmospheric turbulence. But some frequencies are bothered by water in the air. So, a sub millimeter telescope is being built in the Atacama desert, pretty high up.
Arecibo in Puerto Rico is placed in a deep valley so that the supporting structure doesn’t need to be so big. It’s a cost savings thing, mostly. This is the largest single dish in the world.
Optical astronomers put telescopes on tops of mountains to reduce the amount of air they have to look through. That’s not good enough, so some put their scopes in airplanes (Sofia), balloons (Boomerang), or space (HST, Spitzer, XMM Newton, WMAP, Chandra, Swift, etc.).
Where do i put my scope? Mostly my driveway. It’s not ideal. There’s a street light next to it, and a grocery store with flood lights across the street. The disadvantages are mostly the lights, and noise from cars, and stuff. The advantages are that i can set up in 3 minutes, i don’t need to wait for my eyes to dark adapt, i don’t need a flashlight, and if it’s cold, i can go back inside.