I just wanted to ask for some opinions for a CPU cooler (CPU: i7 3770K).
I preferably want a air cooling system.
It would be helpful if you listed the pros/cons of each cooler, like how much heat it draws out of the cooler.
The cooler should be under $50.
(Replacing dat intel stock cooler goodness)
Phanteks PH-TC12DX and Thermalright True Spirit 140 would be other good candidates. The are near the top end of your budget, but will have the most quality. The Thermalright solution will be the quietest, since it uses just one (larger) fan, but it will be the tallest (170mm).
For thermal performance, that is a little trickier to nail down; reviews hem and haw as to which one performs better than the other. They're all single-tower coolers, so performance differences aren't going to be in another class in reference to one another. (With cooling, there is actually a steep measure of diminishing returns. Double-towers see noticeable gains, but in some clases it's "only" in the high single-digits.)