I've got the sony nex6. The 16-50 lens that comes with it isn't the highest quality but it is super compact. I went with sony because I wanted an APSC size sensor giving me a crop factor of 1.5 instead of 2. I picked up the 16mm compact lens and the x.75 magnifier which will give me a nice wide 18mm equivalent as I really like to shoot wide angle. No matter what make sure you get one that has an electronic viewfinder - shooting with just the screen on the back in most lighting is terrible.
A few nice features of the sony include the wifi to phone ability which is handy to allow you to see what the camera is looking at on your phone while you stand in the picture. If you get a cheap adapter you can hook up your old Nikon or whatever lenses and use the feature that highlights what is in focus for your manual focus needs.
I take it with me ski touring and mtn biking. It sits in a case I mount on my shoulder strap so I can draw it out at need.