In Daggerfall, I can never find a Mage's Guildhall that isn't locked. They never unlock their doors. My character is in two joinable factions. The Dibella Temple and the Thieves' Guild. I couldn't get into the Mage's Guild guildhalls even when I wasn't in a faction. Is this just something that guild does in the Daggerfall region?

The Mage Guilds are only open from 11am to 11pm. This is also the case for the Fighters guild and the Knight orders......however...
Any outside door, including these guilds, can be opened by any open spell. If (11pm to 11am) you have an unfinished quest the quest giver (only) will be present, otherwise the guild hall will be empty.

At a certain rank they will be open 24/7, but for now they have hours of operation.

Press 'i' to check the time; press 'R' to and select Loiter to wait.

(Just to throw in a monkey wrench)

I do know of at least 1 exception to this rule...The Fighters Guild in Myrkwasa City, Myrkwasa is open 24/7, even to non-members.

In Hammerfell most Fighters Guilds are actually Fighters Trainers, which is a holy order and open 24/7 just like all temples.

The more you know!