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Wow. That's a very short time, and a long way to go. A weekend in Vegas is a pretty short time, I think, so trying to fit LA & Vegas into one 4-day trip is going to miss a lot.

If you are driving to LA, you should stop in Vegas for about 3-4 hours, take in a casino, then move on. If you're flying into LA, I don't think it's worth it to try to drive to Vegas. It's 300 miles away, and takes 4-8 hours each way, depending on traffic.

In LA:

1 day Disneyland. A weekday, preferably.

1 day Hollywood: Universal Studios, then some time at Hollywood Walk of Fame, Chinese Theater, etc.

1 day at a beach. Huntington and Newport are my favs. Santa Monica is the closest.

1 misc day from the list below:

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.

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: 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. They are currently shooting “Extra” here, M-F 9:00-2:00, so stop by and you might see a celebrity.

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.

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.

Tito’s Taco’s: Voted best tacos in LA, even though it’s in Culver City. King Taco is a good alternate if you can deal with East LA.

The Pantry: Corner of Figueroa and 9th, downtown. Huge portions, they never close, GREAT steak and eggs.

Medieval Times and/or Pirate’s Dinner Adventure: Dinner and an adventure show, both are on Beach Blvd in Buena Park, you get to eat with your hands.

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 Hollywood Heights (formerly Holiday Inn Walk of Fame), all near Hollywood and Highland. 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

It is 282 miles LAX to Vegas, for someone that knows where they're going they can be in Vegas in about 4,5 hrs. For a Noob it will take much longer. 3 nights is not much time to do a lot. I like Death Valley and Joshua tree national park that you get through via Palm Springs but both are off the direct rout to Vegas, If it was me planning this trip I'd head straight to Vegas and maybe explore the Valley of fire about 1 hr out of Vegas. To get to the grand canyon to its closest point from Vegas say to the Sky walk viewing platform takes about 2.5 hrs about 125 miles each way plus the thing cost a small fortune to get on and your not allowed to take your camera on you have to pay someone to take pics for you or buy ready made pics for about $25.it's not worth it. Vegas it self is a blast We've been there 8 times and driven in from SF and La I preferred the drive from SF but that takes way more time than you have. Anyways Use Google maps for some research into your route options and with the get directions tab you can determine the approx, time it will take you. Have fun

Well you should plan the travel according to your budget and how much you can afford to spend so you must be careful it is one of the must expensive city in the world.