Faux wool jackets are pretty hard to find, unfortunately. I really really wanted a peacoat, but they're all made of wool, basically. The best thing to do is just search online until you find one that you like. I did find a few, but most of them didn't fit my tastes.
Same goes for down. Sorry, but I don't know of any off the top of my head.
One last thing: Are you a vegan, or just a vegetarian that doesn't wear things from animals?