At night, the display will be off, allowing you to sleep in complete darkness.  If you wanted to know the time, you could just wave your hand to light the display.  After a minute, the display will go off again.

I see two possible sensor technologies : PIR & radar.

The RCWL-0516 radar module is cheap, offers 360° detection, but consumes 4mA continuously.

The HC-SR505 PIR module is also cheap, has a smaller opening angle and consumes only microamps continuously.  More info can be found here.  It should work on 3V3, but when I do that, it stays in an eternal detection state.  5V is definitely needed.  A comparison of this PIR sensor to another one can be found here.