Emily, I've lived in SF and LA (albeit in the 80s - though I've visited several times in the last few years) and been to Portland a few times recently.
Honestly, I love all three of them, but they're distinct and it's easy to articulate those differences.
LA is spread out and car-oriented. Though, as noted, there are many neighborhoods which have achieved enough density that you could go to a cafe/bar/restaurant in your neighborhood without moving your car. Still. You need a car and you will be spending a lot of time in that car in LA. Great food, both haute and cheap ethnic. Kat has lived in both SF and LA says the Mexican is better down there. The climate is warm, dry (desert-like, really) and temperate. Much more of a beach culture on the west side. Huge latino influence. Lots of cool music (particularly rock) venues and old Hollywood vibes and areas. LA is edgier, a little more dangerous, a little more rock and roll (to me) than SF. But it's also cozier in some ways, since you can get a snappy bungalow in a neat little neighborhod or side-city (like Scrappy's Burbank). Housing would be cheaper in LA because there are many outlying areas. However, you'd exchange your rent cost for your car expenses so I'm not sure that it'd be a huge difference.
Portland would be the cheapest of the three by far. Easy to find cool housing that's affordable. If I were young and had a lot of freedom, I would've moved to New Orleans pre-Katrina. But Portland would have been my second choice. It's one of those places that has both a lot of cool culture and also a lot of room to grow. Lots of musicians who left SF during the dotcom boom wound up in Portland. There is some excellent public transit, but you'd still really need a car. Very outdoorsy culture there. Lots of active cyclists and hikers and runners. Powell's is there, of course. Many cool restaurants and brewpubs and music venues there. Cool and rainy. Quite wet in the winter and gray. Hard on the allergies in the spring. Still - very fun place to go with a combination of Cool Stuff and Cheap Living.
SF - Don't need a car to live here. Expensive housing. Very temperate. Often sunny and gorgeous even in winter. Many neighborhoods to choose from - each with distinct flavors. The Mission, Haight, Castro, Noe Valley. Berkeley and Stanford nearby offering some academic anchors. Half a day's drive from very beautiful scenery like wine country or Tahoe or Yosemite. Strong economy again and hiring. Tons of cultural offerings. Great theater. Decent music. As Cindy notes, there's a strong Boston plus Cambrige to San Franciso plus Berkeley connection. Lots of Buffistas.