What can I do with a free GPS receiver with a coax connection?

Yes, if it can fit up Raeanne's snatch.

The GPS unit will output single-line ASCII "sentences", some of which will contain very precise location and time info (GPS time, that is).

If you're interested, google on "NMEA 0183" to get a list of the things it can tell you.

Isaac

NMEA 0183 is a combined electrical and data specification for communication between marine electronics such as echo sounder, sonars, anemometer, gyrocompass, autopilot, GPS receivers and many other types of instruments. It has been defined by, and is controlled by, the National Marine Electronics Association.

Can I somehow plug that NMEA-compliant cable into my phone? Or into my laptop? Or a desktop?

The wiring looks like it can maybe go to a DB9 but do laptops even have DB9s nowadays?

Yes, it is. And if you look someplace like here:

you can find a list of the "sentences" taht a GPS unit outputs/

You may have to go right to the GPS subunit to get the data, but you can use any of several makes of serial-USB adapters, and any sort of TTY emulator your OS supports. FWIW, I have found ones using CP-2102 and Ft232 chips to be reliable, and ones with the PL2303 to be not so good.

Take care to get the polarity and voltages correct; most of the adapters (but not all) use "TTL-level RS-232", where the logic one and zero levels are inverted from "normal" RS-232. I have no idea what sort of signal levels that particular device emits.

The GPS unit will output ASCII "sentences" which are plain text.

Isaac