West Hollywood isn't exactly walkable and you may find housing prohibitively expensive for a struggling actress unless you want roommates. The southern part of WeHo is "boystown", the very, very gay part of West Hollywood and Santa Monica Blvd is where most of the gay bars and clubs and gay oriented businesses are. It's also the most walkable part of Weho if you want to walk up and down Santa Monica Blvd. The northern part is the Sunset Strip and Hollywood Hills laden with celeb homes. It's true, L.A. doesn't have one central area, it has many. We do have a downtown that was long neglected and is now in the process of a beautiful rebirth.
Walkable and Buzz and not expensive:
Old Pasadena is my #1 choice. ALL my friends from NYC say the same thing: it's the closest thing we have in L.A. to the Village and I have to agree. I like to hang out at the Mona Lisa Cafe on Bleeker Street when I'm in NYC. Anyay, it's a gorgeous walkable urban village just north of Downtown and an easy drive or train ride to Hollywood. Architecture is stunning, the choice of shops, clubs, cafes with sidewalk seating, boutiques, lovely parks, gorgeous tree lined streets with antique street lamps....sublime. You can find quite reasonable apartments here within walking distance of Old Pasadena. It's safe and very clean. I lived there for a few years and would move back in a heartbeat. Some people will say it's expensive and it's not. It's only expensive if you rent an expensive apartment and believe me, they're available. I love it so much I maintain an office there. It has a vibe like no other place in the L.A. area. I had 74 restaurants within walking distance of my place when I lived there 4 years ago. Since I have some time, I'll make you a little collage:
Looking north on Raymond Avenue:

City Hall:

Closeup of facade on Colorado:

Sidewalk dining on Colorado:
Los Feliz is also a nice walkable area. It borders East Hollywood, is very hip and you'll see lots of celebs like Leo and Tobey who both live in Los Feliz. It's not as extensive or pretty as Old Pas but is near many Hollywood landmarks. There's quite a little scene here. I've lived in Los Feliz 6 months (I'm an L.A. native) and I like it here. It's got a great mix of people. You can find reasonable housing here as well (by L.A. standards) despite the fact that upper Los Feliz is a hillside of mansions. Los Feliz also includes Griffith Park and Griffith Park Observatory as lovely Frank Lloyd Wright architectural creations:
Ennis-Brown House

Los Feliz Village along Vermont

Griffith Park/Observatory
Silverlake is walkable just directly around Sunset Junction and has also become quite trendy. I find apartments a little more than Los Feliz's best deals but you can still find something reasonable. Silverlake has long been a gay mecca and is now quite trendy, as is Los Feliz.
Sunset Junction in SIlverlake:

"Silvertop", one of the many examples of Silverlake modernist architecture:

Silverlake Reservoir, where cool people walk:

I think the 3 places I mentioned would serve you well. There are others like Santa Monica but housing may be prohibitively expensive for you.