The Sony Cyber-shot RX100 III is a good option, I looked at it very close before picking up a G16. The G1X may also be a good choice. I use my DSLR all the time as that is what I enjoy most, but these pocket cameras although small, do pack a lot of punch. I carry the G16 for my family gatherings and for times when I want to be more discreet than look like a newsman with all the gear.

My G16 has taken some of my best photos. The new mirror-less cameras can also be a good choice although I would not plan to carry them in my pocket. They do take up a bit more room than the average pocket, but would be easier to carry around. The Fuji Xt1 has been reviewed as very close Image Quality to the best DSLR's. Do the research and make your best decision, there are some FANTASTIC options out there.