Don't know what constitutes "cheap" by your standards but if you want something that is rugged, keeps good time, waterproof (at least to a limit), and doesn't need a power plug... I might recommend looking into a CASIO G-shock wrist watch with solar recharge and water resistance to 20 meters depth. If you get the wave-ceptor model, you can set your international time zone and once per day it will link up with a time reference (assuming one is available in your country) to reset itself using some portable variant of Network Time Protocol. Put it where it would see the direct sunlight at least 5-10 minutes per day and it will run nearly forever until you wear out the strap. I wear one now. It has lasted for at least 5 years so far, and I wore the previous model (fewer extra functions) for at least 10 years before the strap wore out on me. (Special strap because of the waterproof and shock resistance guarantees.) Lesser models lacking the wave-ceptor option DO exist but I like this one a lot.
