The Xiaomi Mi Band 3 is an inexpensive activity tracker. Can you use it without a phone? Kind of. You’ll need an app to set it up; it’s not working out of the box. Once the Mi Band is set up (set the time, update the firmware, indicate which arm you wear it on; the official app requires an account), it works fine without the app.
For what it does, the official app is surprisingly big, and it constantly “phones home”. I first tried to disable internet access for the app, only to find that the app keeps trying and thus drained the battery. There are alternative apps available, some of which much more lightweight and do not automatically send all the information to Mi (apparently these alternatives can authenticate the Mi Band 3, too, but not later versions for which the official app is required initially).
What works without the app? Counting steps, distance (scarily accurate in my case), calories burned; battery left (typically a lot); stopwatch and timer; manual heart rate measure (seems legit). The exercise feature doesn’t work without the phone since the phone does the GPS tracking. Obviously the stats are not available (e.g. the automatic distinction between slow and fast walking, running, and other activity, or the sleep analysis). The alternative apps will calculate these things differently, since only the number of steps, distance, and calories are calculated on the tracker.
Didier Ruedin 
In the meantime we can turn of synchronization with the cloud, and there’s also an option to remove the data and the account built into the app.