The max I am looking to spend is $200. She doesn't need anything fancy
Along the lines of what Stephen Jennings said, you should probably get her a netbook. If you're looking for deals there are some Black Friday ones here, there's a couple of netbooks listed in it for 200.
From the experience with my own sister, I can almost guarantee you that as long as the computer can open a web browser, run AIM, and play Flash games, then she will be perfectly happy. Unless you have other uses in mind, a simple Windows netbook would be a great and inexpensive fit.
I imagine that she would consider small and lightweight to be added bonuses, not limiting factors. She'll easily be able to carry it around and use it anywhere, and there is definitely something to be said for the "cute" factor.
The $200 price limit means you won't be getting anything brand new. Even netbooks are usually more than that. I would watch Craigslist for a good deal. Anything with a P4 or better would probably serve her purposes just fine. As someone above said, anything that can surf the web and play Youtube videos will probably suffice.
My daughter (12) inherited my Dell Inspiron 8200 (ancient, but usable with 2GB Ram and dedicated graphics) .. it works for most things, even simpler games.
A decent & recent laptop can be baught for 600CHF (Swiss Franks) .. I assume that's 400-500$, despite the 1:1 exchange rate ..
So .. buy a used laptop from a hobbyist (like me) .. or get a cheap new one (more expensive, but also more powerfull) ..