I would find a bike that needs a rehab since you might want to either replace or refurbish most of the parts. A cheap mixte with paint (not structural) damage would be perfect since it would theoretically be cheap (theoretically) and a perfect opportunity for a custom paint job that will show her the extra effort you put into the project. I agree, $100 is far too little but with some TLC and smart buying, you'll make a beautiful mixte for a reasonable price. I would prioritize frame quality over others, so maybe a nice Japanese frame (Tange would be great).
A durable clear should make the paint better than most rattle can jobs:
http://forums.roadbikereview.com/sho...d.php?t=231398
If the parts are aluminum, then you can polish them like new:
http://www.bikeforums.net/showthread...1#post11841802
Then all that's left would be maybe new tires, a bell, basket/rack, wires, gears. Depending on how many hills there are there you can do a single speed or a rear derailleur only type of thing, to keep things simple. I found out that a lot of females appreciate the "look" more than anything.
I personally would make something as close to this as possible:
But a lot cheaper.