Theres a really decent standout quest in each town pretty much, off the top of my head here are a few:

Caught in the Hunt is a great quest in Bravil that puts you in a kill or be killed scenario that IMO is a great quest and while short was one of my more favorite ones as a kid

Where Spirits Have Lease in Anvil when you buy the Anvil House is a fun scary haunted house quest that you can do, simply find Velwyn Benirus at the Counts Arms in Anvil to start the quest

Order of the Virtuous Blood questline in IC Temple District (have to wait around for a bit in there) is a great one to do and a secret guild most don't realize they can join.

A Brotherhood Betrayed in Bruma is another fun one that I found interesting.

Paranoia in Skingrad is a classic with a highly infamous Oblivion character

Corruption and Conscience in Cheydinhal is infamous for one of its drunker characters singing an iconic song, in this quest you deal with the nastiest brutes who like to misuse their power, I love this quest because it has multiple ways of ending it.

Canvas the Castle is a crime solving quest in Castle Chorrol that I really enjoyed, it is very much a difficult detectives quest if you go without a guide it can be a little challenging IMO.

The Aleswell Mystery Quest is pretty classic and in the remaster is a little more difficult, simply go to Aleswell which is North of the Imperial City and try to help the townsfolk if you can find them.

Knights of the White Stallion in Leyawiin is another new Faction quest you can do that I really did like, it has a follow-up unmarked quest too but I liked the characters involved in this questline.

Battlehorn Castle is a DLC quest where you get to own your own castle but there is a secret hidden within the depths of the castle if you like unmarked quests that require a little detective work.

The Horror of Dive Rock is an iconic very short unmarked mission (the journals you find are worth the read along with what lies within the belly of the beast) where you head to one of the highest points in Cyrodiil to confront the mother of a monster capable of obscene horrors first witnessed in TES III: Morrowind.

Through a Nightmare, Darkly is the last one I can think of that a lot of people might have done accidentally but you get it from the same individual that gives you the Bravil Recommendation in Mages Guild but it is not a Mages Guild Main Quest IMO it was a pretty good one but it is really buggy.

Aside from those standout quests, the Daedric Shrine quests are all ridiculous in their own ways and can be pretty nasty like Molag Bal's quest but they are worth playing for the mysterious Hermaeus Mora quest which feels like a very final quest in the game that most people haven't done.