In reply to Andrew W:
I use a Ricoh GR, which has a fixed (prime) 28mm equivalent lens, which also features 35mm & 47mm crop modes in camera (reduces quality though still more than acceptable due to the large sensor).
I am sure have seen them for around your budget, I have the GR 1, which does not have wifi. I did purchase the lense adaptor to allow filters to be fitted.
I find the image quality fantastic with the APS-C sensor, and the pictures edit & export nicely in lightroom.
I find the 28mm lens to be very versatile for the shots I like to take, people and landscape. It is very intuitive to use and fits into a small case. I am hoping to give it much more use over the spring.
I am sure would be suited for climbing pics if you can live without an optical zoom. I was after SLR image quality, in a compact camera body, and it seems to tick the boxes while costing considerably less than the Fuji X100 alternative I initially found.