Los Angeles can be done on almost any budget, though of course your experience will reflect what you are able to spend. As long as you don’t plan on multiple theme park visits then you can keep costs under control by taking advantage of doing free things at the beaches or elsewhere. If you do plan on one or more theme park or studio tour visits, you should probably see if the Go Los Angeles Card is a good deal for you.
If you have access to a car then you’ll be able to do and see much more in far less time, and a cheap rental might save you money in other ways since it’ll allow you are greater choice of food and drink options. Trying to visit using only public transportation means moving slowly or limiting yourself to just a few neighborhoods.
Food is relatively cheap in Los Angeles, and there are plenty of great budget choices among the various ethnic cuisines you’ll find in most areas. Some of the local fast food chains (like In’N’Out Burger and Tommy’s Burgers) are both cheap and very worth trying, and prepared food and ingredients are easy to find at the many supermarkets spread all over the city.