I'm gonna second this recommendation. You can get last year's entry level DSLR and a normal zoom as a refurb or open box for under $400 and it'll take better quality pictures than pretty much any current pocket camera model. If you're frustrated by modern smartphone cameras (which are on the low end performance wise as far as pocket-sized cameras go), most compact P&S models aren't going to be a huge improvement. The cheapest DSLR will make a night and day difference in terms of focus speed, focus accuracy, exposure accuracy, and image quality. Compared to a pocket camera, a DSLR (even in full auto mode) will get you more keepers and fewer photos ruined by the camera being too slow, bad exposures, poor dynamic range, and so on.
Also, don't be fooled by bogus megapixel and ISO ratings. While many pocket cameras claim to have enormous numbers of pixels, the optics and focus accuracy are very rarely good enough to make every pixel count. As a result, the effective usable resolution could be be half or even a quarter of the advertised number. ISO sensitivity is similarly exaggerated, with most pocket cameras producing snowy, washed out looking pictures well below the claimed maximum sensitivity. On the other hand, a 6 or 8 megapixel DSLR really does provide the claimed number of distinct pixels and on last year's DSLR models, ISO 1600 and often ISO 3200 and beyond will produce perfectly usable pictures. Even if the lighting is bad and you totally mess up the composition and have to crop out 80% of the photo you'll still have enough left to post on the web or make a small print that's not embarrassingly bad.