My favourite camera system is still micro four-thirds from Panasonic and Olympus! There's plenty of super small bodies (eg Lumix gm1, gx800 or the Olympus Pen E line) and thin lenses to choose from. So you can really go for a super compact setup, which is also easily upgradable. And you can adapt pretty much any vintage lens!
There's also nikon 1 and pentax q, which are similar concepts but even more compact. And especially the former can be found for very cheap on ebay. Haven't used those two myself tho (yet).
If you want to go more into the fixed zoom lens direction I can recommend the lumix lx100 and people really like the sony rx100 line.
Unfortunately the premium point and shoot market feels like it's almost dead at this point but there are soo many great ones out there on ebay from a few years ago when camera manufacturers still cared about that segment!