I have an S5200 and have been generally pleased with it, although I'm soon to make a move to dSLR-world. The S5200 has very little shutter lag, unlike many P&S models. However, it does *not* have the image stabilization that the S2 and S3 have. In addition, I find the flash to be unreliable. I have made some decent flash pix with it, but some have been terrible. Beyond just a very few feet, it's basically useless. On the other hand, its ISO800 capability is really very good for such a low price point. ISO1600 is pretty noisy, but might be the difference between a "noisy" (grainy) shot and no shot at all. I should add, too, that there is something of a learning curve involved, in order to get the best results, so you should spend some time practicing with the Fuji, should you decide on it, before you hit The World. Be sure to get adequate memory card(s) and a couple sets of rechargeable AA batt's. Battery life is very good, though. In six days in the parks in July 2006, I never ran a set "dry", although I always carried an extra set, just in case.
Examples of what the S5200 is capable of, even in the hands of a non-pro:
http://s76.photobucket.com/albums/j11/fasteddiew/DisneyWorld 2006/
Feel free to visit any of my other albums, if you like.
~YEKCIM
Edit: Have you considered Fuji's S6000fd, or is it out of your price range? It is a big improvement over the S5200 in many ways. A buddy of mine has one and says it is awesome.