In fact, Los Angeles of the first half of the 20th century had an extensive system of streetcars, cable cars, and funiculars (of which only Angels Flight remains in semi-functional form) which were systematically eliminated specifically to facilitate the the freeway system, which was designed for distributed suburbanized growth. Trying to build a really functional public transit system in Los Angeles today would require so much right of way, would run into geographic obstacles, and would meet so many legal and environmental challenges that it is kind of amazing that it actually has the Metro and Metrorail systems it has.
‘Tremendously’ is a relative term. While it is true that the Los Angeles Metro system has expanded in the last decade and ostensibly provides access to most of Los Angeles County and even eastward proximity to a stop and limited operational hours pose limits to its utility. Part of that problem is that Los Angeles is just not a ‘walking city’ and many areas are actively hostile to pedestrians (and I say this as someone who has walked around and between major parts of the area) so even if you are close to a stop ‘as the crow flies’ you may end up walking a few miles to get there. Buses can be useful but aren’t great and tend to be more off-schedule as the day goes on. Transit is good for getting from and to certain venues and locations like Dodgers Stadium or Hollywood & Vine, but not generally for getting around in the way that, say, the Chicago “L” system or the New York subway system is, and certainly isn’t comparable to the London Tube or other modern public transit system in high and medium density cities in developed nations. On the plus side, though, the Metro is generally quite clean and pretty safe. Definitely research your trip because instructions on how to get from one place to another that require exchanges are often unclear.
As for the o.p., I have to concur with posters that the daughter needs to plan on using taxis or (ugh) Uber/Lyft. Even if age weren’t prohibitive for renting, the traffic in Los Angeles is one of the worst aspects of living there, and while LA drivers are not the most hostile I’ve seen (hello, Boston!) they have a tendency to be inattentive or treat traffic laws as suggestions, which I suspect drivers from London would find to be outrageous. Parking is also a massive problem especially around some of the venues mentioned in the o.p. and unless you know where and how to park you can spend more time and money that it would be worth in terms of taxi/rideshare costs. I’d recommend making a list of things that she wants to see and grouping them together geographically to minimize time-in-transit.
For the places listed in the o.p., the Griffith Observatory is well worth doing (one of the best views in the city and generally on the short list to take people visiting the city), and especially if you can do it at night. The hike up to the Hollywood sign, on the other hand, is…not worth it. The Hollywood Walk of Fame is about 15 minutes of mild amusement. Searching out filming locations can be challenging just because so many things change that after a few years many of those locations may not exist, so definitely research that. There are a lot of beaches if you don’t mind the crowds but I agree that Santa Monica Pier and you can rent a bike and pedal down Venice Beach from there which would make a nice day out. There are a lot of good museums (LACMA, the Gettys, Expo Park) but if I were going to do just one I would recommend the Huntington Gardens and Library in Pasadena (also a popular filming location for anything set in botanical gardens so that could be a two-fer). There isn’t a lot in downtown that is tourism-friendly but if she’s going to try using the Metro Union Station is basically the central hub and is worth at least walking around in, and you can basically see anything else worth seeing within a walk of the Pershing Square and Civil Center stops on the Red Line. Chinatown is one stop up on the Gold Line but don’t expect to be too impressed (although there is good authentic Cantonese food as well as many other cuisines if you know where to find it).
It isn’t clear what support she’ll have from her host family but if you can it would probably be good to get hooked up with someone similar to her age and interests who could make specific recommendations and even facilitate some of the exploration. Despite how popular it is for tourism, Los Angeles isn’t really that great of of city to go and tour around in on your own recognizance beyond the obvious tourist traps like Disneyland, and most of the best stuff is in local neighborhoods like Los Feliz or outdoor activities like hiking in the various foothills and nearby mountains.
Stranger