I would go with:
1) Greenlake
2) Ballard
3) West Seattle
As a general rule, the further out you go, the less expensive it will be... Here are the best areas of town:
Arm & Leg Expensive:
Beltown & Sodo: Really preppy, downtown
Queen Anne: Kinda preppy, on the edge of downtown
Montlake: Pretty neighborhood near UW.
Expensive:
Magnolia: On the water, should almost be included above.
Ballard: Cool bars, home of the tatooed/pierced crowd...
Fremont: Hippie town
Northlake: Meh...
Capital Hill: Known for it's gay community, but is across the freeway from downtown. You can find occasional good deals here.
Greenlake Yuppie-ish but not too bad - my girlfriend lives there...
Ravenna: I haven't spent too much time there to have an opinion...
Wallingford: Sort of across I-5 from the U District. Has a strip of bars and restaurants along 45th (I think).
Spendy:
Greenwood: Lots of crime, but up and comming neighborhood.
Shoreline: Like Greenwood, but with less crime.
West Seattle: Some cool areas. Has Alki Beach. Gets worse as you go south.
Magnuson/Sand Point/University Village: Some good deals here and there. Good access to I-5 and Lake Washington.
Further out:
Alderwood
Lynwood
Edmonds
[This message has been edited by Pierce County Ag (edited 12/7/2009 2:38p).]
[This message has been edited by Pierce County Ag (edited 12/22/2009 2:20p).]