The next part of my nixie tube clock is some kind of real time clock that can keep track of time. The DS1307 is tiny and does just that. While the final clock may use GPS to get an accurate time, odds are it will be used to set one of these in case GPS reception is lost. The clock seems accurate - it's kept time for a day at least!
I'm using the AVR's TWI hardware rather than Wiring library's I²C code as I may not use an Arduino in the final clock (but they're really handy to prototype with!).
The LCD shows pretty much what the nixie tubes will: date and time, both six digits.