The bathroom in our house does not have enough light where it counts, on your face as you stand at the sink to shave, etc. We live in a rental so I cannot put in a new fixture wired into the house. I've been looking for LED fixtures that run on batteries, but I figure they will not be very bright and will need the batteries changed too often.

I thought I'd check on here and see if anyone has any good ideas for bright, directed light without wiring.

There is an outlet nearby, though running a cord to it would be ugly, I'd live it if I had to I guess, but would prefer not to.