Being *simple* likely depends on your ability to search for existing designs, hardware, and software. Are you wanting to develop your own circuit board, or build a clock by wiring together existing boards/modules? Are you trying to avoid writing firmware?
I like the Arduino movement since it creates a lot of AVR processor boards that I can use for dirt cheap, even though I never run firmware using the Arduino libraries or built in the Arduino IDE.
Everything I do is for a hobby. I want to focus on my application and not putting effort into a board design that I may only use once, and my retired eyes don't like a lot of intricate wiring. Tying functions together with an i2c interface makes it easy to hack together something like a clock using existing modules with minimal wiring.
These days, an i2c-based DS1307 chip is commonly used for the real-time-clock (RTC) function. You can use a DS1307 chip on your own board design, or find any of several small prebuilt boards using one. I personally prefer the more precise DS3231 that I can set and forget.
I have various clocks and time controllers using an AdaFruit Boarduino running my own AVR firmware, an AdaFruit chronodot RTC board using the DS3231, and an LCD display with an AdaFruit i2c-LCD backpack. For an LED display instead of the small character LCDs, I've thought about trying one of the AdaFruit alphanumeric i2c LED arrays like this red one -
https://www.adafruit.com/products/1911. They have various size i2c-based 7-segment displays as well.