I just bought an Olympus Tough TG-1 with a built-in GPS. It seems to work well, only taking a few seconds to aquire a fix after turning on. It may take longer if the camera has not been used for a few days, or transported some distance turned off, I don't know.

Apparently it can use A-GPS to speed up aquisition but that is not available to me where I am, anyway it works fine without it. Location data and the direction the camera was pointing when the shot was taken is all in the EXIF.

Oh yeah, images are passable although background detail (foliage etc.) shows heavy smearing. Colours are accurate, exposure is reasonable too. I have yet to test the waterproofing etc.