Azoth
Okay, so Threnody and Thaka are along. You in, Theo?
I'll try a few things before I try bashing the door.
I yell up to one of the windows (if there are any...) that I am Azoth, priest of Apollo, seeking entrance.
If that fails, I try walking around the tower to see if there's another entrance. Are there any sea-caves or anything that might lead into the tower from underground?
If all else fails, I try an open doors check. 1d6 BR 1. Sweet. What's inside?