The Apple Watch does not display its local IP address in the settings for some reason. Here is one way to get it, if you have a second Mac on the network.
- Open terminal on the mac, run
python -m SimpleHTTPServer.
- Get your Mac’s local IP address (option+click on the network icon in the toolbar).
- Send yourself an iMessage with text
- Turn WiFi off on your iPhone. This is important because the Apple Watch can use your phone’s WiFi.
- Open Messages on your watch, find the message, tap on the link.
In the terminal on your Mac you will see something like
192.168.0.21 - - [12/Oct/2021 12:00:00] "GET / HTTP/1.1" 200 -.
And there you have your Watch’s IP address.