Here's a website describing some of the LAUSD choices:
http://echoices.lausd.net (Charter, HG Magnets, SAS, etc.)
I've heard mixed reviews about the gifted magnets but mostly positive about the HG magnets. Some are elementary only and some go through high school. If you look at the criteria for the gifted magnets the required scores may be lower than you would expect,
http://echoices.lausd.net/Magnet/GiftedCriteria.aspx, so an LAUSD gifted magnet may not get you were you want to be (to the person that mentioned HG/PG), but perhaps a HG magnet would. I have also heard mixed reviews about the Mirman School, specifically that they are great with MG kids but (like many other schools) they are less great about accommodating the needs of PG kids. I don't have any personal experience with that school, this is just based on comments from friends who did have personal experience.
There are also lots of other resources available in Los Angeles - early college opportunities (Cal State LA's EEP program, for example), lots of community colleges where younger kids can take classes, summer programs like SIG at UCLA or CTY in Pasadena, Westlake and LMU, etc.
There are also many very good school districts in/near LA but not a part of LAUSD, like San Marino USD, Beverly Hills USD, Palos Verdes USD, La Canada USD, South Pasadena USD, Las Virgenes USD, Arcadia USD, etc. Some of the smaller suburban districts have fewer specific gifted programs but offer more in terms of regularly accelerated curriculum (like IB, AP, etc.) If you need info about a particular area, PM me and I'll give you whatever info I've got.
The best private schools in LA, and even some of the not as great ones, are very expensive (as an example, tuition at Harvard Westlake School, grades 7-12, is near $30K). Also if you want to send kids to one of the best private schools expect to have to compete with lots of other families for limited slots!
