I turned a 1980 model "portable" TV from Goodwill into a little clock. I removed the now-useless broadcast tuner and deciphered the remaining circuitry well enough to determine where to inject sync and luminance signals. These signals are generated and bit-banged by an ATmega8 AVR.
The clock also contains an old wifi router running OpenWRT in client mode, so it can attach to my wireless network and sync to the 'net using NTP. The wifi hardware then continuously sets the AVR. The clock displays local time on top, and UTC on the bottom. So to set the timezone, you just log in to its web interface over the wireless...