It says "No info" in the sunrise/sunset dial, bottom middle.
I pressed where it says "No info" and it told me to add a location on my smartphone. The screenshot below is from my smartphone at this point:
I added my location but it told me I had previously done that! I tried many times but no luck. It was still saying "No info" on my S3.
On the smartphone, open the Samsung Gear app:
Press Settings | Apps
On the Apps page press the Weather cog/gear icon (as shown above)
Press Use current location
Make sure it is set to On (as shown in the example above)
NOTE: Before setting it to On do read the message on the 'Use current location' screen (shown above). Make sure you understand what it will do, if you are worried about your location information being used by others then do not use this feature.
After setting 'Use current location' to On, check your Gear S3:
You can see in the images here that the sunrise and sunset is shown in the dial on the watch face.