The ring doesn't have a GPS so it doesn't send any location information. However, as long as the ring has some battery left, you can use an app called 'Find my Bluetooth device' to search for the ring.
When the ring is near the app, you will see that on the app. Different apps can be found from AppStore/PlayStore and at least some of them are free of charge.
You may also want to contact your insurance company to find out if you can receive any compensation from them.
If you suspect that your ring may have been stolen, there's no need to worry about someone else accessing your data. If someone attempts to connect the ring to another device, a factory reset of the ring is required which will clear any data from the ring.
Learn more: What does "Restricted mode" mean?