A lot of the point and shoots clump into categories, often conveniently around your price range.
There are a bunch of weatherproof cameras, but they sacrifice some utility for that feature, and are a bit pricey for what you get (I have the Panasonic TS5; love it).
There are what they often call "travel cameras" that are pretty easy to use, have a decent zoom, are very small, and often have features like wifi (handy for sharing on the road) and/or GPS.
Superzooms are also popular; they look kinda like SLRs, and are bigger and bulkier. But they have huge zooms, and take pretty decent pics. Popular especially with those who do outdoor stuff, wildlife etc.
Some point and shoots have features, like RAW capability, more manual controls, and the ability to add like a flash. Some concentrate more on wifi features, a hot topic these days. Samsungs, for example, seem to almost have more in common with phones.
In general, the last one or two models behind the current one are often great deals. Folks geek out on all kinds of megapixel specs and such, or bells and whistles like GPS or higher def video or more wifi features, so if you can live without that you can do very well.
Also generalizing, I'd say the Panasonics often are a bit better at video. Canon has a super wide range of cameras, and their firmware is hackable, so even an old Canon can do amazing things if you're interested in longevity. Nikon and Sony also make some great units, as does Olympus. It's sorta hard to go wrong.
Just as an example, CostCo right now in the US has a Panasonic Z35 and a Nikon CoolPix S6800, for US$200 and 229 respectively. Both would do fine. They also have a Kodak superzoom for that price.
I'd decide on a feature or features that you think would be most useful to you and your intended uses, and then go from there, like telephoto, video, GPS, etc.