Find my Mac: "Online, no location available"
Solution 1:
Turning on Wi-Fi did the trick for me.
My MacPro's location wasn't showing up. It is connected to the Wi-Fi router via ethernet. I turned on Wi-Fi (to the same router), and my MacPro's location now shows up in icloud.com under the Find My iPhone pages.
Solution 2:
I just waited a while, and it started working. There's no indication of why it wasn't working at one point but then started working later on. That's kind of concerning, because I wonder how reliable the system is. But there doesn't seem to be any fix beyond "wait it out".