Dark Brotherhood. Definitely.
Aside from that, anything that fits the character. All of the faction quests are reasonably interesting.
Oh, also Shivering Ilse, because that's fun in a psychotic fever dream sort of way.
Finally, ffs, Morrowind was not that much better than Oblivion. I started the series with Morrowind, loved it and dumped close to 1,000 hours of my life into it. Then Oblivion came out and I dumped roughly the same amount of time into that. The two games are different, yes, but they do different things right.
When I heard Skyrim was coming out, I tried replaying the series (I even got Arena and Daggerfall off the Bethesda site, but those things are so unwieldy by today's standards that I gave up). 10 hours into Morrowind I was so bored or traversing the same areas 50 times I switched to Oblivion. And then got bored 10 hrs in because of the stupid enemy leveling.
That being said, my boredom was simply due to how much time I've put into them both. My point is, I've played both game recently and I still can't tell you which i like more. They're both extremely good games. Why can't people just accept that?