Hyrule Castle Tower/No Logic
The Hyrule Castle Tower is commonly known as Agahnim's Tower in a rando context.
Getting there
You will usually enter the tower through its front door, which normally requires the master sword or the cape. With a bottle and a mirror, you could conceivably get there using Barrier Revival.
You can also reach the top floor of the tower by carefully performing a west subtile YBA from the hourglass-shaped room in Misery Mire (NL). Perform the YBA (toward the room with the wizzrobes and the big key door), back out exactly 2 or 3 pixels, then transition west through the door.
Getting around
You don't need any keys to open the two chests. A north subtile YBA in the first door will bring you to the 2F dark room, skipping the first key door.
With this, you can also reach the Agahnim fight with only one key.
Where you can go
You can clip out of the Agahnim fight with a bomb to reach Hyrule Castle Escape (NL). This is useful as a step of dungeon ID swapping that will make the game believe you are in Swamp Palace (NL).
A spin subtile YBA north from the "circle of pots" room brings you to the Vitreous fight. The fight will have some strange properties that you can see in this Twitch VOD.
Getting a dungeon prize from Agahnim
If you are in another dungeon's state when you defeat Agahnim, you can receive that dungeon's prize. It is reported that you then have to walk inside a building before you save and quit, or else SRAM will be corrupted in a way that deletes your save file.