Ive always wanted a non-combat quest centered around a dungeon. Where there are still enemies, but you have to use the traps in teh fort to kill them, or you have to get through various scenarios like becoming a ghost and finding a willing person to let you possess them before you can return to your body.
Here, I'll try one:
In the city of Falkreath, citizens whisper that one of its women is feeling troubled. Investigation leads to an elderly Nord widow. This woman tells you that she's unsettled because she's been visited in her dreams by her dead husband, who complains about the company he's had to endure lately - she gets too frightened to tell you anything more about his plight, but gives his name. She asks for you to visit their ancestral tomb at the graveyard outside of town, and gives you a key. And she gives specific instructions not to disturb the spirits.
So, you enter the tomb. It is a moderately small undead dungeon. There are ghosts, but they are passive - if you attack, they will retaliate until you cast a calm spell, go invisible or leave the tomb. And they'll spawn in large numbers to make it difficult. You walk around to search for the husband's grave. Reaching it, you notice that the lid to the coffin is off, and that something appears to be missing inside... There's no corpse! You see tracks leading toward a passage, and a crumpled note that looks like a shopping list. It says "Fresh clothes, check! Tea set, check! Tea, check! Friends to play with, still pending." It seems someone is having their way with the dead in this tomb.
You follow the passage, which is a tunnel leading back into town, ending in a basemant. There, you see a couple skeletons dressed up in frilly dresses and hats, seated around a tea set on the table, posed just so. If you follow the stairs to the main floor, you discover the house's occupant, a Khajiit. He looks very embarrassed at being discovered, and is quite talkative as a result. Through the dialogue, you can either choose to ( A ) attack him for being so deviant, ( B ) report him to the town guard and to the widow, ( C ) agree to help him cover it up, so long as he puts the corpses back and doesn't do it again, or ( D ) encourage him to continue. The results being:
A ) He dies. You get access to his little house, and the widow thanks you for putting things back in order by giving you 100 gold, while maligning the Khajiit's fate.
B ) You go to report him to the guards, but he is nowhere to be found, and his house is now locked. The widow thanks you for putting things back in order by granting you the husband's rare (but unenchanted) shield.
C ) The widow thanks you for putting things back in order by granting you the husband's rare (but unenchanted) shield. The Khajiit is grateful for your help, and gives you 500 gold.
D ) The Khajiit marvels at finding someone as necro-friendly as him, and offers you 100 gold, his bed at any time for free, plus a rare book that raises your Necromancy skill. The widow, meanwhile, is incensed and wants nothing more to do with you.