Can I turn the display off without putting the computer to sleep?
You can use Hot Corners to put your display to sleep instantly. This article on OSXDaily walks through the steps, Quickly Sleep the Display in Mac OS X with a Hot Corner.


Launch System Preferences and click on “Mission Control”
Click on “Hot Corners…” in the lower left corner
Set the screen corners you want to use to “Put Display to Sleep”
Close out of System Preferences and test the Hot Corner by sliding your cursor into that screens corner