Earlier quoted context omitted.
I used a wall "atomic" clock for a couple decades. It would synchronize itself with a government radio signal.
WWVB is great if you can get the signal -- I have two of those clocks in different rooms, and only one of them synchronizes.
If you have AM-based clocks, you might find that these work better. However, nobody advertises which module they're using, so it's kind of a crapshoot. I specifically bought a phase modulation WWVB receiver and it reliably receives the signal every night. I also have a random $7 clock from Amazon that pretty much synchronizes every night. Living in NYC, this is truly amazing to me; I never ever got the AM signal here.