There are literally hundreds of things to do here in LA. Here is my list of “must sees”. Visit as many as you have time for.:

Disneyland: The Happiest Place on Earth. Half a billion visitors can’t be wrong. #1 Destination.
Universal Studios: A theme park that grew out of a studio tour. #2 Destination.
Even if you don’t visit Disneyland or Universal Studios Tour, Downtown Disney District and Universal City Walk are very fun places to visit for shopping and eating. And they’re free to visit.

Hollywood: Enjoy the Walk of Fame, Entertainment Museum, Chinese Theatre and more. You can see a lot for free. The Hollywood & Highland complex has lots of shops and restaurants, and the Kodak Theater. The El Capitan theater, right across the street, is where Disney shows their movies. And the Hollywood Bowl is a GREAT place to listen to concerts outdoors.

Olvera Street/Union Station: Olvera Street is the birthplace of LA, and it emphasizes our Mexican heritage. In addition to the Avila Adobe (oldest building in LA), you can eat at some pretty good Mexican Restaurants, do a little shopping, and taste a churro. If you don’t want to go to Tijuana, this is as close as it gets without going there. Union Station has great architecture from a bygone age. Also, you are 2 blocks from Phillippe’s (see below).

Rodeo Drive, 90210: Packed with exclusive shops, full of gawkers. They all came to enjoy the excess. Free, unless you intend to buy something.

Venice Beach: Los Angeles kitsch and over-the-top culture at its best. Here you’ll find Muscle Beach, street performers and tacky shops galore. Fun, VERY interesting, but I avoid it after dark, when it gets a little TOO interesting for my taste.

Santa Monica: Beach and Pier: Great beach scene and a classic seaside amusement park, complete with antique carousel that has been in a lot of TV and movies. After visiting the pier, you can ride a bike south a couple miles to Venice Beach.

Sunset Boulevard began as a route between the stars’ posh neighborhoods and the Hollywood studios. It runs from downtown to the ocean, passing through the "Sunset Strip" on its way.

Farmers Market and The Grove – A new shopping complex right next to a Los Angeles landmark, It is right next to CBS, so walk across the lot to see if they are taping "The Price is Right". You might even get in.

Griffith Park – Home of the Los Angeles Zoo, Griffith Park Observatory, Travel Town, the Greek Theatre, and Gene Autry Museum of Western Heritage.

Getty Museum – The Getty’s architecture is so beautiful that it keeps me fascinated. No matter whether you like their art, architecture, or view better, the Getty is sure to please. Free.

Attend a TV taping – You can get free tickets at audiencesunlimited.com, tvtix.com, or see the booth at Universal City walk. It’s very interesting to see a show being taped. The most popular, by far, is the Tonight show. Check the NBC web site for all the details there.

Places to eat:
In-N-Out Burger: Multiple locations, best burger in LA, ask anyone.
Pink’s Hot Dogs: 709 N. La Brea, just north of Melrose. You might even see a celebrity. Maybe.
Tommy’s Chili Burgers: Look for the shack, an LA tradition. The original location is at Beverly & Rampart, a couple miles west of downtown.
Canter’s Deli: 419 N. Fairfax, between Beverly & Melrose. Near CBS, you might spot a celebrity.
Phillippe’s: 1001 N. Alameda. Great roast beef sandwiches. Near Union Station and Olvera Street. Watch the mustard, it’s hot.
Tito’s Taco’s: Voted best tacos in LA, even though it’s in Culver City.
The Pantry: Corner of Figueroa and 9th, downtown. Huge portions, they never close, GREAT steak and eggs.

Places to Stay:
Since LA is so spread out, there is no single place that is close to EVERYTHING. Most people who come here tend to stay in Hollywood, Santa Monica, or Anaheim. In Hollywood, I recommend the Orchid Suites, Hollywood Celebrity Hotel, or Holiday Inn Walk of Fame, all near Hollywood and Highland. Another one is the Best Western Sunset Plaza. In Santa Monica, the Holiday Inn Santa Monica is close to the pier and reasonably priced. In Anaheim, I recommend the Howard Johnson (HoJo) Anaheim, and the Candy Cane Inn. There is also a nice place in Burbank called the Best Western Media Center, very close to Warner, NBC, and Universal Studios.

Places to Shop:
Third Street Promenade, Santa Monica
The Grove, Los Angeles
Americana @ Brand, Glendale
Beverly Center, Los Angeles
Citadel Outlets, Commerce
Brea Mall, Brea
The Block at Orange, Orange
South Coast Plaza, Costa Mesa
Fashion Island, Newport Beach
Santee Alley, Los Angeles

Day spas: Glen Ivy Day Spa

Obviousman has covered a good portion of what there is to do. I just have a question for you. Why are you doing a week in Vegas? Do you have a plan on what you are going to do because Vegas is just one town and after 3 days I’m ready to leave. California is much bigger. Why don’t you dedicate more time to California and visiting more that there is to do. It’s just my opinion but a week in Vegas (unless you are doing shows every single night, finding things to do during the day and going to the Hoover Dam.) Whatever you choose, good luck and hope you have a good time!