Welcome. LA is a great food metroplex.
The absolute best is the LA Weekly with Pulitzer Prize winner Jonathan Gold. It publishes every Thursday and is available on-line. Beyond that, there is the LA Times Wednesday food section, which is pretty hit or miss.
La Weekly: www.laweekly.com
There are some neighborhood papers (City Beat, Hollywood Independent, Larchmont Chronicle), but most are pretty flimsy. There is also the LA Daily News, which covers the San Fernando Valley and might be helpful if you live in that area. Food-wise, though, the Weekly is definitely the big fish in town.
In addition to LA Times and The Guide, and LA Weekly, If it's "scene" you really want, follow the blogs.
This is mine, and it's a good amount of aggregating from most of the LA area blogs and papers, plus general dining news, gossip, openings, closings, etc.
Pat (who also responded to this post) does a great job with ethnic eateries, especially on the east side of town (Silver Lake, Los Feliz, etc.
Different people, all sorts of restaurants, pretty straightforward reviews of new and not new spots
Multi-authored, many topics, but the food section keeps tabs on restaurants an dining
Metromix, another Tribune product, skews younger, but stays on top of trends and openings
There are a lot of neighborhood rags and blogs, but decent for scanning. Unfortunately, LA Magazine isn't fully online yet, and the Daily News, which mostly covers the Valley, isn't easy to follow, but they are there. Patric Kuh in LA Mag is a solid reviewer, as is Brad Johnson at Angeleno magazine (also not online). LA has a completely different food media market than in New York.
LA Times gets a lot of grief from the 'Hounds here, but they have a posse of really good food people, possibly the equal of the NY Times food staff. No big stars like Bittman, but Russ Parsons is I think in Bittman's league as a cook, just not so openly a maestro. S. Irene Virbila, as she styles herself (Ruth Reichl, who used to work with her, just refers to her as Sherry in her books), is commonly known as SIV in the local posts, and her restaurant reviews get argued over a lot. As with so many critics she is often at her best when she's scathing, especially when she manages to all but dismantle some Palazzo of Pretentiousness without ever saying one technically negative thing. As for the non-restaurant content, it's every bit as good as NYT's Food (see above), and I think better presented and usually more entertaining.
sku is right, though, about J. Gold and his writing in LA Weekly. The only other weekly I see on a regular basis is my local Pasadena Weekly, which while not as pathetic as it used to be (they're down to just one writer who thinks a tortured style denotes literary brilliance) it's only marginally useful, unless you're willing to accept PF Chang's and The Cheesecake Factory as palaces of fine gastronomy.