Olympus OM-1 (or OM-1n) if you can stand using silver oxide batteries for the light meter. There are many other great fully mechanical options but they can be somewhat expensive or have issues with finding lenses. The OM-2n is also great but the shutter requires a working battery and it's actually a very complex camera internally (it does real-time aperture priority metering by measuring the light reflected by the film surface while the shutter is open, if you want it to).

A Nikkormat FT3 or Nikon FM would also be good choices, but I like the compactness of the Olympus.