My experiences with neighborhoods:
Downtown: too expensive, don't bother
Capital Hill/First Hill area: High paced, loud, full of 21 year old kids who think they are better than you in every way. If you like to party fucking hard, don't mind assholes, and don't mind it being loud ALL the time, then this is cool. Most people who live here, do it for 6 months then move on.
U District: Super Cheap, you get what you pay for. Cheap eats, cheap booze, not as loud and active as Capital Hill, but it has it's nights. I lived there for 9 years and enjoyed it for the most part. It's close to everything for busses and whatnot.
Northgate: Where I live now. It's quiet, and about as cheap as the U district. Most of the people up here are in their late 20's/early 30's, still a bit of partying, but not too bad. Low crime, but theres plenty of seedy characters hanging around (see: Bobcat and I)
I would gladly live in the Ballard area, although it seems like it's kind of becoming the new hip place of town for meatheads to hang out. It's still really nice through most of it. Scandanavian culture, cheap drinks, plenty of places to eat and hang out. Mostly quiet!