Lost or Stolen Devices:
If your device has been lost or stolen and you
have not installed a Find your Device application there could be a slim chance that your device is still on and has Data enabled. Therefore you can access your Gmail/Google account via your computer and go to the Play Store and install an application, possibly from the list below onto your device. If this works you can have a chance at locating your device.
If you feel you are out of options, before buying a new phone, please make sure to tell your carrier that your last phone was lost/stolen so they can properly deactivate it.
Otherwise, if you
have installed one of those applications then you can use that to find your device, simple as that.
Here are some recommended Find your Device applications:
Where's My Droid - FREE
Lookout Security & AntiVirus - $2.99/m
SeekDroid - $2.99
Prey Anti-Theft - FREE
Avast! Mobile Security - FREE
These are just a couple I have heard really good things about.