If we were all still shooting film, I'd say something like a Kodak 127 format. That's about as no-brainer as it gets. Fixed lens, fixed focus, single shutter speed, cartridge film. The slightly posher ones even had a variable aperture.
There's currently very little out there that matches what the OP wants. It's all about bells and whistles these days, and I totally get what the OP is saying - too *much* functionality is a right pain. I have a Canon Ixus 60 that I picked up for £12 in CEX last year. I had to cough up another fiver or so for suitable memory cards (won't take anything bigger than 2Gb) and a reader, but it does it for me when I don't want to take one of my DSLRs out and about. Let's face it, a 1D is not exactly portable or inconspicuous.
Ironically, the least faffy cameras around are the pro level ones but then you really do need to know what you're doing as they don't have any of the, erm... "idiot modes"
I would suggest a bottom end DSLR with either a 28, 35 or 50mm prime lens depending on sensor size and how "wide" you want your field of view to be. If you leave the camera in full auto mode, it is then essentially the same as one of the old-style rangefinders, with the exception that you have AF. Bottom end DSLRs are by far the smallest and lightest, and a prime lens wouldn't add much bulk to the overall package.
BTW, I really dig Canon's 50 1.8 mk2 prime. It might be their cheapest lens, but please don't let that fool you - it's a little cracker, pin sharp, virtually no chromatic aberration and being a 50mm which "sees" at the same viewing angle as the human eye, there is no distortion. I've had mine for 20 years and wouldn't swap it.