I have a Legolas-inspired character that I want to be quite planned out. He is obviously an archer who can dual wield daggers and also use a sword for blocking, but I would like to get archery to a high level early in the game. Later in the game-play some sneak perks too.

These are the things he will do:

Get all three shouts for whirlwind sprint

Get all three shouts for elemental fury

Get the aetherial crown

Do the main quest

Some dawnguard quests

do the civil war quests

Angi's training

What other things would you suggest for this character to keep him occupied? Nothing evil though, it is a good character. I find archery in Skyrim to be quite awesome, so I would like to keep this character going for a while.

You should destroy the Dark Brotherhood, break up the skooma ring in Riften, defeat Potema in Solitude, drive the vampires out of Morthal, kill the cannibals in Markarth, kill the butcher in Windhelm, and save the people of Dawnstar from their nightmares.

kami has obviously been here before. There are some thugs at Nilheim that need tending.

That'll keep him busy. I could see him doing that-rooting out evil wherever it may be.

Trials of Kyne.
Get Zephyr for rapid fire archery.
Acquire all 3 words of slow time. It slows down the rest of the world more than it slows you. Relatively, you go a lot faster. It's like elemental fury but it works on bows too.

Absolutely! I had a whole thread, not too long ago, about must-do quests for a paladin type. I forgot - there were some good ones out on Solstheim as well. You don't have to be Dragonborn to do them either. I think there was one to stop the Ash Spawn, one for re-opening the ebony mine, and one for rescuing the smith from the Skaal village.

Don't just do some of the Dawnguard quests, do them all. You want that bow! Many people are also fans of the ancient falmer armor, although I am not, personally.