Yosemite is great to do once in your lifetime, but it's likely going to be a zoo during the season. The real gem of the southern Sierras imo is King's Canyon and Sequoia National Parks, particularly the
Rae Lakes Loop, all 40 miles or just a piece of it depending on time available and your pace. Popular as well but it's not going to be as jammed as Yosemite, and you can truly find wilderness, solitude, and some epic views on this hike. You really can't go wrong in this region, it's all great.
If you are a fan of desert views, both
Telescope Peak and Mt. San Jacinto have extraordinary prominence. You can see basically all of Death Valley from Telescope Peak and San Jacinto has great views as well-- on a clear day you can see all of Southern California's mountain region from San Jacinto. These hikes are slogs, however, so be fit. If you are a masochist, try the Cactus to Clouds Trail on Jacinto-- 10,400' of elevation gain, among the highest amount of traversed prominence to be found on any single peak approach in the world. In June, the valley shouldn't be full of smoke but I'd check before you do either of these hikes so the view isn't ruined by haze.
If you like ghost towns, the
Panamint City hike via the surprise canyon trail is a good challenge and imo makes for one of the best ghost town experiences in the US because you're very likely to be the only person there. Fun scramble up a creek, too. Watch the weather.
Route 1 from LA to SF is known as the Pacific Coast Highway, or PCH, and is a world class drive. Big Sur is a gorgeous region worth a stop, and if you've got $$$, I can't recommend
Post Ranch Inn highly enough, especially if you're with a ladyfriend. It's something else.
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I don't have much good to say about San Francisco proper as a destination, except when it comes to food. Yank Sing is some of the best dim sum you're going to find in California, and Sushi Ran, in Sausalito, some of the best sushi. Sushi Ran is Michelin star I believe, and deservedly so. On a sunny day, Mt. Tamalpais to Stinson Beach is a beautiful hike that offers some great views of the city across the bay. You have the option to park in Stinson Beach, uber up to Mt. Tam, and hike back down. Needless to say, don't leave valuables in your car anywhere near SF lol