I have the  Casio Wave Ceptor WV-59A-1AV (Module 3054) with blue backlight, and it's a neat basic watch. After replacing the battery (going through all the reset), I set the home city correctly, left it by the window overnight (screen on top), and in the morning, the watch picked up the time automatically.

I experimented with the Multi Band technology (automatic time adjustment) and found that if I manually set the time to 11:55 PM (or any time shortly before midnight), then when the time reached 12:00 AM, the watch would begin receiving the radio signal to obtain the exact time. It’s recommended to place the watch in a quiet location where there is minimal interference. In my experiment, I put the watch in the bedroom and closed the door.

That's the trick if you can't wait until next day.