I usually goof around on the computer if I haven't actually gone to bed yet, or, if I'm lying in bed awake, on the phone. I have a Kindle but it's not backlit so I don't usually read it at night... however, there is a Kindle app on the phone, plus all sorts of games and whatnot.
On the computer I use an app called "f.lux" which changes the color of your screen at sundown, so it's MUCH gentler on the eyes. On my Android phone the app I use is called SunSpot which basically does the same thing. That's really helpful for lying in bed playing on the phone... I don't have to turn on the lamp, and I still have enough light to see what I'm doing, but it really reduces eye strain. So when I am ready to doze off, it comes much more naturally because my screen is orange rather than blue. It's something you don't really notice while you're using it, but if you turned it off you would see a big difference. Anyway, it's a huge help!
