I can't quite figure this out.

I'm in Ky's Tower, and I've mapped the entire maze, bumping into the walls.

I was pretty sure I missed something, so eventually I looked online and saw there's supposed to be a door where my party is facing. But I just get a wall.

Cheating further, I found that I was supposed to answer a riddle, but I was never posed the riddle (the endless byway one).

I can't apport, and none of my Phase Doors have been successful.

Anyone know a way out other than reloading? Oy.

There's another exit to the maze, towards the north east (it's likely how you entered it). I believe it's a secret door, so you need to cast Greater Revelation (or Lesser Revelation) for it to be visible during the brief flash of light (or to see it from the other side).

If all else fails, you should be able to get out by death warping; just kill off every member of your party and you will be sent back to the Adventurer's Guild. (Of course, the downside is that everybody will be dead and you will need to find a way to bring your party back to life, but depending on the situation, that might be preferable to reloading.)

That did it! I brute-forced through the northeast and found the door you mentioned: I guess I hadn't been as thorough checking all the walls as I'd thought. Fortunately, there aren't a ton of random encounters: my mages' spell points were almost retired.

This tower is when you should start finding a Mage Staff in random loot. Get one of them for every mage in your party, as they regenerate 1 SP in each round of combat, and also at certain intervals when not in combat. They will extend the amount of time your party can stay in a dungeon for a long, long time.

Agreed that Mangar 1 is a better place to look for them. There are a lot fewer darkness zones, anti-magic squares, and teleporters. If he has the key, that makes it even easier to get into the tower so he doesn't have to go through the sewers.

**************some spoilers*************

In these games, it's important to move into every single square on the map because in one of the squares you leave unexplored might be whatever it is you are looking for or you need to progress in the game. Also, running Sorcerer Sight, for instance, will show you secret doors on your map, whereas spells like Cat's Eyes, while providing more light won't reveal secret doors--but there are other spells that will.

On some levels in the game, apport arcane and phase door, for instance, will not work because the dungeon owner (in this case, the mage Kylerean) has deliberately disabled certain magic spells on certain floors.

The riddle comes from a magic mouth. If you have not been posed the riddle, you have not hit the square with the appropriate magic mouth...

Unless something changed in the remaster, Sorcerer Sight doesn't reveal secret doors; you need a Conjurer (or, in BT1 only, Magician) spell to do that. Of note:
In BT1 and BT2, PHDO and APAR either are both enabled for the entire floor, or both disabled for the entire floor. In the versions of BT1 I've played, there is one exception: You can teleport into Mangar 3, but can't teleport within that floor or cast PHDO there.

In BT2, if there is a Death Snare on the floor, you can't use PHDO or APAR there (though you can APAR to a teleport-allowed floor, of course).

In BT3, the rule I stated doesn't apply; there are places where one spell works but not the other, and there are even times where one of the spells might work in some spots but not others. (You will actually need to make use of these two spells at some point in BT3 to progress the game, though PHDO can be replaced with Wall Warp.)

Incidentally, Dragon Wars (a game that was originally intended to be Bard's Tale 4, though I find it to be a very different game) has a PHDO equivalent, and that spell is actually mandatory and very useful there. Or it might lead to a stasis square that you can't get out of for a long time. (This happens in a couple spots in BT1, and happens frequently in BT3, though it's much easier to get unstuck in 3.)

I only remember the stasis square in the Catacombs. Level 2, I believe? Was there another one somewhere that I missed?

I believe there's one in Kylerian's Tower, though the game does give you a hint about its location.