Similar to the Daedra, my understanding of the Aedra is that they are a bit more benevolent. So, I was curious if they might have some quests better suited to a Paladin.

The only quests related to the Divines are the ones from the Temples.

I'm not a huge Lore-Buff but I do know the basics, I'm pretty Omega or someone else mentioned that the Aedra cannot communicate with the world like the Princes.
Although I'm not 100% on this.

There aren't any purely Aedric quests that I'm aware of. Typically, throughout ES history, the Aedra are much less...direct...in the affairs of mortals.

There are quite a few quests that involve the worshipers of the NINE in one way or another. For example, healing the Eldegreen in Whiterun or helping Erandur to clear out Nightcaller temple are the closest you'll be able to come.

There are the quests for the temples of Dibella and Mara which have some helpful rewards, ie. permanent "blessings" if you'd like to think of them that way.

Oh yeah? I've only managed to get one of those blessings. The one from Mara. Ironically, they said it would help with women, but all it does is help me do extra damage against them. XD

Where are the others?

The Aedra are dead. They can't really interact in the same way as the Daedra. They still influence the world though, and every now and then an avatar of them might show up.

The extra damage vs. opposite six is the Dibella blessing. Mara blessing gives you permanent magic resistance.

A few Aedric related quests I could think of:

Runil is a priest of Arkay in Falkreath who has you do two minor quests:
http://elderscrolls.wikia.com/wiki/Runil

And of course Erandur, a priest of Mara, in Dawnstar with his quest:
http://elderscrolls.wikia.com/wiki/Erandur

There's the quest for the temple of Dibella in Markarth:
http://elderscrolls.wikia.com/wiki/The_Heart_of_Dibella

Kyne's Sacred Trial (Kyne is the Nordic name of Kynareth):
http://elderscrolls.wikia.com/wiki/Kyne%27s_Sacred_Trials

Those come to mind. There are possibly some others. Also, you could consider just going around and doing good deeds even if they aren't related to an Aedra. Like clearing out necromancers and undead which some quests will have you do.

My absolute favourite quest was the Wolf Queen one I got in Solitude. There needs to be more of those. Made me feel like a real damn hero.