There's a little icon next to your XP bar which indicates when you're in a Sanctuary. (Generally, it's anywhere with an Aetherite, but that icon will indicate if you're really within range of it or not.)

Originally, the three starter cities were inexplicably exempt from that within-range-of-an-Aetherite rule, and the only part of them that counted as Sanctuary was within the Inn, but now the entire city is considered Sanctuary. I still log out from the bed in the Inn if I'm in any of those cities, but there's no real need to anymore. Now it's just because it sort of feels right for my characters to go to sleep whenever I'm not playing them.