I made one of these GPS -> WWVB simulators a couple years ago. There's a short write-up here, in case anyone is interested in reading about it: https://www.anishathalye.com/2016/12/26/micro-wwvb/

There are also some neat iPhone apps that use the audio circuitry to produce a low-power signal that can be picked up by radio-controlled clocks that are close by: https://itunes.apple.com/us/app/clock-wave/id1073576068?mt=8

A couple people mentioned the FCC and licensing issues in the comments below. As far as I know, as long as you're transmitting at a very low power (40 µV/m as measured at 300m), it's okay. This should be fine for personal use, but won't work on a municipal level.