LA is pretty much a different country. When you get off the plane and start exploring you will find out that everyone in certain areas dresses like a runway model or they are wearing jeans and a sweatshirt no matter what the weather is. Of course you are going to want to visit Hollywood boulevard which I do recommend seeing at least once but there is so much more that LA has to offer.
Melrose avenue is famous for being a shopping, dining and entertainment destination. They have amazing Tobacco Stores and clothing shops which are truly original. Many tv shows talk about Melrose avenue. A popular one that attracts a ton of people is LA ink. You cannot just walk in there expecting to get a tattoo right away. Instead you should call up months before time to reserve your spot. Who knows, you may even end up on the show depending on the difficulty of your piece and who you chose to do it.
The Hollywood sign can be seen from miles away. It has been a fixture of Hollywood for decades and it is not so easy to get up there. The sign is protected by security and fences but you can get pretty close and see an amazing view of the whole city.
Downtown LA is filled with a ton of skyscrapers but that is not why you would want to go. Every city has skyscapers for the most part but during the weekend there is a ton of outdoor flea markets and amazing food trucks. Most of the culture in these outdoor markets is Mexican so if you are looking for authentic Mexican food then this is the place to go.
Universal studios is great for both locals and tourists. If you buy a ticket it is good for the whole year so many locals love to just buy the ticket and go a few times a month. The best way to get there is by taking a city bus is subway to the universal stop and then you will find shuttles that take you there. You do not just go to universal for the rides as there are a ton of restaurants outside of the park to explore.