Two solid recommendations, but they might be a bit pricy.
Canon Powershot S110. Solid camera-very popular for vlogging on the go. Pretty solid-can survive some punishment. Lowest price I've seen is $159, but typically is around $209-249.
Sony DSC-RX100. The best pocket camera on the market. 1" sensor, Zeiss glass and all around great camera, but at a much higher cost. $550 is pretty typical. The updated version (RX100 II) is $699 with slightly better light sensitivity and the addition of a hot shoe. Keep in mind that the cost of this camera is pretty much in the same range as a Canon 60D, so you're definitely in DSLR range.