After a lot of research I bought my fiancee the Sony RX-100 recently, and she took it along on a week's holiday (I joined in the 2nd half - ie the last 4 days of the holiday).
I have 2 Canon DSLRs, but I know that my fiancee, Ali, wouldn't want to have a big camera for most of her purposes (though she has used my DSLRs time to time). It is very compact and good body quality.
The Sony RX-100 is an impressive compact... bigger sensor than any other camera in that body size, and images are very usable at ISO1600, and reasonable at 3200, and still ok (if really required) at 6400.
Don't expect to match a FF in terms of DOF control or pure IQ, but compared to any other compact P&S cameras, it's very good. Each of the 20MP are sharp (good lens, great sensor).
It has plenty of customisation - and for Ali to play around with / learn settings, etc. The only gripe I would say is that macro is at wide angle only (ie it does great macro at wide, but can't focus close when the lens is zoomed in... bit of a shame, but still, we captured some excellent wildflower and even insect photos.
I prefer optical view finder - but then again, the Sony RX-100 is very capable, and has a good screen. The Sony Rx-100 vII has just been announced, with some minor improvements, but 95% of it is the same.
I'm very happy with my purchase, and Ali is thankful with her present. I trust my contribution helps.