I don't mean to disappoint anyone but we've found that LED nightlights work well. They provide enough light for the kids but we don't have to worry about them playing with them like flashlights.
I've seen some LED nightlights that also serve as emergency flashlights called the Eco-i-Lite. The light runs off wall power until a power outage and then the battery takes over. The light is removable from the plug/cradle which inductively charges the battery.
Short funny story and plea for safety. The other day I grabbed my little Peak Shasta off my dresser to take a look at something. The problem was it didn't turn on at all. This was odd since it was perfectly bright (for it) the day before. When I pulled the battery out I noticed that it was in backwards. A quick check showed that the voltage was very low. I remembered that we let our 4 year old take a nap in our room which has AC. He quickly admitted to taking it apart and that it didn't work after he put it back together. I was worried about the LED/circuit but it evidently has reverse polarity protection since it worked fine with a new battery.
Plea for safety - please make sure there isn't anything that an infant/toddler/etc. could choke on. My boss had a friend whose baby choked on a coin for just a few minutes and suffered permanent brain damage.
My 2 year girl loves to grab my lights and look under the sofa or whatever. She really wants a pink light (and a pink knife but that's a different story). I really don't like buying cheap made in China stuff (for various reasons) but I'm not comfortable with something like a Mini-Mag or Solitaire that she could take apart. I suppose she would be safe with the HDS EDC but she can barely push the button and it's not pink.
Regards,
Rich