Look for a sewing machine like this one. It's hand-cranked. My wife learned to sew on a machine like this and picked one up a few years ago for $90 "just in case" something needed sewing when the power was out. A lot of sewing machine repair shops will still fix this style, especially if you find a Singer or other popular machine. I like this style when I'm just doing straight hems. It's slow, so the accuracy is higher than the electric sewing machines.

-Blast