I've had luck with Travelocity and Priceline. For airline tickets, also check the websites for the carriers that fly to LA. (Look into flying into Burbank, too. It's a much smaller and easier to navigate airport. I hang out a bit at a small travel forum, and a lot of the folks there use Priceline for hotels. Priceline is good if you're not set on staying at a particular hotel. The people I know who use Priceline also use a lot of Frequent Flyer miles and take a lot of trips to nowhere in particular (buying cheap tickets) just to rack up air miles. Then they redeem all the miles for things like First Class upgrades to Europe.
LA is spread out over a very large area, so most of the attractions are not within walking distance of each other. (And not all of the attractions are in LA itself.) I think you'll be wanting to rent a car. Public transportation here is not easy for the uninitiated. What are some of the things you'd like to see or do? Some of us locals could likely steer you the right way.
I've not taken any of the guided tours around here. I think the main ones are the tours of Hollywood. I suspect they'd be fairly interesting and entertaining, but I'd look for a reputable-looking company. (Maybe ask at your hotel.) Hollywood has some cool landmark buildings and things like the Walk of Fame, but for the most part, it's now a pretty seedy part of town. The main streets (Sunset and Hollywood) have some pretty touristy sections, a few upscale sections and some pretty dodgy sections that you probably don't want to walk at night.
You may want to check out one of many beaches. They range from upscale (Huntington) to strange but fun circus sideshow (Venice) to somewhere in between (Santa Monica). Lots of people-watching to do, shopping for everything from high-end stuff to $5.00 t-shirts, and of course there's the ocean. (The water will be chilly. It'll be foggy or cloudy for much of June.) Here again, let us know your tastes and we can likely give you some suggestions.
There are the amusement parks like Disneyland, Universal Studios, Magic Mountain, and Knott's Berry Farm. All of them are different, but expect to spend $55 to $65 plus $8 or so parking to get in the gate. Other places like Universal Citywalk, Old Town Pasadena, Third Street Promenade, and The Grove have a wide range of shopping and dining places, geared towards pedestrian traffic. They are free, but expect to pay $8 or so for parking for these places.
There's the La Brea Tar Pits (and the museum there), the Peterson Automotive Museum (tons of cool cars), Getty Center (high-end art), and a bunch of other good museums. (I've not been to any of them, and I've lived here for almost 17 years.)
More kinds of restaurants than you can shake a pancreas at. Nightclubs of all stripes. Churches of all denominations. Strip malls. Strip clubs. Movies out the kazoo. The Zoo. Descanso Gardens or the LA Arboretum. Whale watching. Deep-sea fishing. Sea World (a couple hours south in San Diego). Vasquez Rocks...you can go hiking where they filmed a ton of westerns, and most of the "alien planet" scenes in the original Star Trek TV show. Concerts from A to Z. Or, just sitting on the beach doing nothing.
Like I said, let us know what you're interested in doing or seeing, and maybe we can give you some ideas.