hmm ... that's an interesting idea...
could probably be done with microcontrollers ... each clock display would have a pic in it to drive the LEDs and request time from a master unit, using some sort of low-speed serial connection ... really only need data and ground - the displays don't need to send the master any information, just receive it.
the master unit would also have a pic in it along with some buttons for you to set the time with, and something like a serial real time clock (with a battery backup!)
programming would be the hardest part of this project, not to mention, having wires running all over the house!
how about this idea instead... you have indiviual clocks, each clock has it's own pic and real time clock, runs off batteries or mains voltage... each clock has a jack on the back with a few pins - that can connect to another clock just like it.
so you set one clock to the correct time, and then take it around to all the other clocks and connect them - maybe a switch that is "master/slave" or something ... plug a slave into a master and the slave synchronizes with the master to the correct time.
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I just try to keep the number of clocks down in my home, to avoid resetting them all the time! ... the computers reset their own clocks with software, and my clock in the kitchen is radio controlled, using some "time signal" the goverment produces or something.