I believe it should ask you to use your location. It took the notification some time to pop up on my phone after setting up the Astronomy Homescreen for some reason. It just kinda randomly appeared when I was using safari asking if you want to allow Astronomy to use your location.
Mine looks good in the preview, but then goes fuzzy once actually set as the Lock Screen. Also, the depth effect works in the preview with the time behind the earth, but once set, the text is on top of the image for me.
I consistently had trouble in the first beta. It would constantly revert to California. So far with the second beta, it has stayed on Ohio. It was on Ohio as soon as I swiped to that lock screen.
Of course, now there's an ugly green dot on my location that is (1) there on the home screen, (2) there when my phone wakes up with a locked screen, but (3) is not there when I pull down the lock screen on an unlocked phone.
The close up view doesn't show the cloud cover which defeats the purpose for me. But strangely for Sydney there is another zoom level between full globe and close up view that only shows for the Home screen wallpaper that has the clouds, there seems to be no way to set that view for the lock screen.