The '$200 or less' requirement pretty much absolves any hope of a decent ILC. Best bet would be to find one of Canon's S-series (S110, S120) refurbished, used, or on sale.
That's fine. I don't want to have to fuss with different lenses. While I appreciate that's the best way to get exactly what you need for the shot, I just don't want to have to do it. I also have no qualms with getting something refurbished, if that's what it takes.
I can spend more, I just feel like 200 bucks should get you something that can take decent photos.
A phone can take decent photos- a $50 compact with a zoom lets you zoom. Unless you're willing to pay up for an S-series, spending more than $50 either gets you more zoom or a smaller camera, like Canon's ELPHs.
A word on sensor sizes- every basic P&S has a 1/2.3" sensor. The next step up is the 1/1.7" sensor found in some higher-end models like the S-series and Canon's G16, which is larger and has manual controls. Above that is the 1" cameras like the Sony RX100/RX10 and Nikon's 1 system, which has interchangeable lenses.
At best, while keeping a decent budget, reaching for the 1/1.7"-sensor cameras is worth the cost. Just have to catch them on sale.