Lots of bedside clocks do emit a lot of light. I wanted a clock that can be read easily, but does not light up my entire bedroom, and uses very low power.
Using an ESP8266 (Wemos D1 mini) , an 1307 RTC and a 0.96" OLED I now have what I wanted! The ESP is in deep-sleep mode for a little over 59 seconds, waits for the time to become HH:MM:00 and then sets the hands on the OLED in the correct position.
The RTC allows the ESP to go into deep-sleep but still keeps track of the time. I found that the deep-sleep timer of the ESP is not sufficiently accurate to be used as a clock, so the 1307 RTC was added.
In order to get a low amount of light the brightness of the OLED is set very low.

In total this clock only uses 3 mAh, my previous clock without RTC and without deep-sleep used 75 mAh.