Congratulations on the job and the move. I'd rather live in NYC but LA ain't bad.
I refuse to believe that commute is the first and foremost important factor in where you live. To which I ask this question : How old are you? single? married? kids?
This is much more a determinant of where you should be looking to live. Also the types of things you like doing (do you prefer being outdoors? Or care more about restaurants and nightlife) etc.
If you have kids, scratch out West Hollywood or any residence that falls under the LA unified school district. Amongst the most underfunded and poorly educated kids in America. You'll be paying 15k per kid through 12th grade for private school, which you will be slammed into a waiting list to enroll in anyways.
If you prefer spending your time at beaches, hiking, biking, whatever, stick with the coastal towns. I'd go with Santa Monica, Marina Del Rey, or Manhattan Beach. I work in SM and it's nice, though I'd never live here. MB is pricey but the entire white collar work force in LA lives down there. Marina Del Rey is just chill. You literally cannot typecast that town or its inhabitants. I lived there for 4 yrs thru college.
Getting to Downtown from SM will pretty much be the 10 freeway which can suck hard. Getting there from MDR or MB will be the 105 E to the 110 N which can also suck hard. It's simply a bit too far to take entirely on surface streets.
If you're young, single, like going out, wanna meet girls, you can't beat WeHo. I live on Doheny and Beverly which is very central to any restaurant you might want to try, any lounge/club/bar etc. Lot of cute girls, easy to navigate the town via side streets even through rush hours. Downside is that a lot the girls you meet here, though reasonably easy to talk to, are utterly vapid and have nothing but crap for brains. Commute to DT is easy enough. 35 mins in tough traffic by simply bombing down Olympic. Before you know it, you've already gone through KoreaTown and are in front of Staples Ctr. You can also take Beverly all the way to DT (the northern end of it).
Someone said that Silverlake and Los Feliz are like Brooklyn/Williamsburg. Totally true, but you also have the conspicuous hipster that actually makes 6 figures and only cultivated his/her hipstery image because they had the money to spend. There are a lot of struggling actor/artist types here, but you have as many wealthier entertainment people. Producers, writers, actors etc. But you'll be the only dude in town with a suit on for sure. My sister lives here and I never let her hear the end of it. You're pretty close to DT from here, although most any drink you order in local bars will be served to you in a goddamn mason jar, by some guy who likely makes his own small batch artisan chocolate/coffee/compost fed herbs.
You mentioned Valencia. Yea, live there if you want to get depressed and kill yourself. That drive alone is wretched enough to begin to think about. And it's like suburbia. Only with a heat index equivalent of the finest wood burning ovens in NYC. It's probably easier to live on one of the nearby stars that orbit our earth.
No one mentioned Brentwood and West LA. Both areas are large and predominantly filled with young professionals and young-ish families. Mostly very normal people. It's probably a bit like the upper west side. It's closer to DT by 4-7 miles than Santa Monica coastline and it's further from DT than Beverly Hills/WeHo by about 2-6 miles.
I guess as long as I'm making comparisons.
Silverlake/LosFeliz/ = Brooklyn/Williamsburg
Venice Beach = Lower East
West Hollywood = Meatpacking/Chelsea
Beverly Hills/Bel Air Estates = Upper East
Hollywood Blvd = Times Square
Hollywood = Midtown
Westwood = Murray Hill
Downtown = Financial District
Valencia = think the most boring suburb outside of Manhattan.
Santa Monica = West Village
Santa Monica North = Greenwich Village
??? = Hells Kitchen
Runyon Canyon/Beaches/Griffith Park Observatory/Malibu/Malibu Canyon/Big Bear/Silverlake Reservoir etc = Central Park
Park La Brea = Freaking Stuyvesant Town