Basic design of the clock

For this clock build, I've selected the following components:

An ESP8266 based microcontroller board. I've picked the Wemos D1 mini because it's cheapish, I've used it before, and it's easy to program via USB. It's also wifi capable, so you can send it messages etc and make it display something other than the time if you like.
An eBay sourced DS3232 RTC with backup battery to provide the time for the clock.
5mm neopixel LEDs to backlight the tubes for a nice visual effect.
IN-12 nixie tubes because they're cheap, but you can use most types with a few tweaks.
An ebay sourced TINY 170V DC-DC converter that takes 5V in, and outputs 170V to drive the tubes.
Discrete NPN/PNP transistor drive using MPSA42/MPSA92 transistor pairs in SOT-23 form factor.
Four PCB mounted switches for setting time etc.
An LDR to allow the clock to dim in response to changes in ambient light.
74HC595 surface mount shift registersx2 to provide the right number of IO lines.

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