I'm about to start a new character, this time a mage. I've not played with magic at all yet so it should be interesting. However, instead of going straight to the College of Winterhold I want to do a bit of 'free-lance maging' sort of thing. So my question is, are there any quests (other than from the College) which deal with magic or magicians? Even collecting herbs for a herbalist would do.

If there are some, who do I need to speak to to get the quest? Please try not to spoil the quest if you're posting about it

Thanks in advance!

College in Winterhold is a really nice place for a budding mage and the first quest is not hard at all, and very doable for a very early level character. You have multiple side quest givers there and pretty much everybody there will have a nice quest that's well suited for a magic user. I think a mage will do well going to Winterhold early. But if you don't want to go there early, the mage in Rifen will have a fun little fetching quest. Farengar, the wizard in Whiterun's Dragonsreach will have a tiny "menial" delivery task for you. Visit alchemy shops in different cities and many will have pretty substantial quests. One in Windhelm, and another in Riften and maybe one in Dawnstar and maybe also one in Falkreth. I can't quite remember. And there is an interesting sidequest in Dawnstar that's also pretty nice for a mage.

Note that alchemy is part of stealth school, not magic school, although it is a very powerful complementary skill for a mage.

A scroll for Anska is one of my fav magic quest things. At the end you get the spell tome Flaming Familiar. It runs into your enemies and explodes, which is always fun to watch. :3

edit: Also, North? Of Whiterun is a bandit dungeon called Halted Stream Camp, in it is a tome with Transmute Ore. Lets you turn iron into silver, and then into gold.

The quest Infiltration grants you the tome Detect Life, which you otherwise need a high-ish level of alteration to get.

I don't remember any other quests/locations that grant you spells.

I... really have a hard time with Flaming Familiar.... I don't like that the familiar explodes....

Not far into the College quests you are required to go into a level 15 dungeon/cave/tomb. I did that at level 11 and it took forever and I died a lot. RIGHT AFTER THAT they tell you, "Quickly, you must go here and retrieve this special thing" which is in a level 24 dungeon! I had to walk away and still haven't been back. I'm level 23 right now and can feel the doom approaching....

You mean the books quest? Ahh... on my first character I died so much that I hated the place. Also, I was new to the game and hostile mages jumping out of everywhere seemed... weird.
It's still one of my least favorite parts of the questline.