Almost any GPS receiver outputting 1 pulse per second (1pps) will meet your 1mS tolerance. I say almost as I certainly can't vouch for all of them!
A simple downsteam module with either a hardware division system could show and distribute time-of-day once synced. Obviously a PIC-type processor board could also read the NMEA data stream for time etc, and use the 1pps for syncing, then distributing TOD by the method and in the format you choose. Which is a faster-to-fruition system depends on your micro skills vs hardware design and implementation. Some time later (not in your time window unfortunately) I will be using a PIC 16F877 dev board to do something very similar behind my GPS-derived frequency reference unit.