Just replaced my S100 with a Canon G7 X for less than $500 ($650 new, but I always buy used). It's a bit bigger than the S100, but still pocketable for me. The much larger sensor and wider aperture, plus features like focus peaking (highlights in-focus areas when focusing manually) and hardware exposure dial make the larger size totally worth it.

The features I miss from the S100 are built-in GPS, CHDK support (which the G7X may get eventually), high-speed video (though I rarely used it), and the super-secret tiny size.

Researched this camera for several months before buying, so here's my notes:

The G7X and the Sony RX-100 mkIII are almost exactly the same for general-purpose photos. The RX-100 mkIII has an optical viewfinder and bounceable flash, both which would help if you're doing mainly portrait photography, but that's not me. The Sony has an artificially limited AEB range of +/- 0.7 stops, which is kinda useless if you want to do manual HDR, but does have 120fps video. The G7X is a bit cheaper, and has the hardware exposure dial, a longer zoom (and wider aperture at full zoom!), touchscreen focus, and built-in astrophotography modes (star trails/etc.). It's fast taking pics out of the gate, but full RAW continuous mode is just as slow as the S100 was (~1.5 shots/sec), which is kinda embarrassing when my 5DmkIII-toting brother borrows it :P

Since I focus more on landscape, star, macro, and abstract photography, the G7X worked out best for me. If you're doing more portrait and sports (or pets/kids) photography, you may lean towards the RX-100.