Apple - Put the display to sleep without putting the whole computer to sleep?

You can turn off your iMac (and your macbook) screen without sleeping via the following keyboard shortcut:

⌃ + ⇧ + ⏏

(Control +SHIFT + EJECT)

Machines like the Air and newer MacBook Pro with no optical drives have the power button in the same place as the eject key and it works similarly for display sleeping shortcuts.

In Terminal.app:

pmset displaysleepnow

https://developer.apple.com/legacy/library/documentation/Darwin/Reference/ManPages/man1/pmset.1.html

This also works for the lock and sleep functions:

pmset sleepnow
pmset lock

Your first stop should be the energy saver preference pane. Dial down the Display sleep slider as short as you can stand it.

If you don't want to wait for this time out, you could also set a hot corner and black screensaver so you could use VNC to set the mouse pointer to the corner to engage a black screensaver so the screen is as dim as possible until the sleep timer shuts off the LCD lighting as well as the data to the iMac screen.