Anyone out there have any solo missions, or possibly duo missions online? I'm looking for something to run alone with the characters, to give them a taste for the game and get a little character development going. Anyone have any ideas?

Solo missions are much more dependent on the character in question than the regular team missions, so it'll be difficult to come up with ideas without knowing anything about the chars. At least the archetype has to be known, as solo chars naturally just can't do quite a lot of stuff.
I for one know of no generic solo missions online.

Hmmmm. I can understand that. My fault.

Main one would be for a mystic adept, mainly focusing on unarmed combat with the spells mostly being telekinetic type abilities. The character isn't a combat monster, but is fairly inept at social skills, being very open, brunt, and not really keeping much of an internal monologue.

I recently ran a solo mission for an adept in my group. He wanted to learn Ninjitsu, and I didn't exactly want to make that a "pickup and go" skill since its supposed to be secret. So, I had him follow a trail of clues that he was given that put him through increasingly difficult tests.

* First he went to a Dojo and the Sensei there gave him a workout that nearly killed him in order to test his dedication.
* Then he had to climb to the top of an abandoned refinery in the barrens that was guarded by Barghests on the perimeter. He had to climb to the top using several climbing and jumping tests (difficult for him with a Strength of 2).
* At the top his was attacked by a martial artist and hand to defeat him in hand-to-hand combat.
* Finally he had to sneak into an apartment building guarded by the Triads and plant a black Rose on the pillow of a man sleeping there, all without being seen by anyone

Feel free to rip it off for ideas. However, like Dragnar said, solo missions are very much tailored to the person who will be the player in the mission and are mostly about character development.