I recently made these notes for an AUS friend:
NYC
To see the Statue of Liberty from the water, ride the Staten Island ferry over and back. (Don't waste time on the SoL tour.)
The Intrepid Sea, Air & Space Museum is a very good tour. Shuttle is there, plus view across water to NJ. Many aircraft on display including the Concord.
http://www.intrepidmuseum.org/Eat NY cheesecake wherever and whenever you can find it. Also NY bagel with cream cheese is a must. (Lox is fish like sardines, so beware of ordering that.)
Deli sandwich, best are at Carnegie Deli. One sandwich will be enough to split. They are huge and absolutely delicious. (Counter servers can be very rude, but keep calm and carry on.) It's a good place to get NY cheesecake too. Pizza, the one recommended to us as the best in NY, is Vezzo Thin Crust, "shrommtown and meat lovers." It's in midtown.
http://www.vezzothincrust.com/ But, pizza is on every corner.
Don't eat the street food. It's tempting, quick and inexpensive, but don't eat it.
Natural History Museum and MOMA are worth doing. MOMA has many masterpieces. Don't miss Van Gogh's Starry Night.
Walk in Central Park. It's huge.
For LA, my advice is not to over-plan. You'll spend a lot of time in traffic if you divide your time among far-apart locations. LA is a working town, not a tourist destination. Where you decide to stay will probably determine what you're able to do in a short period of time.
For SF:
Take the half-day trip to Muir Woods. It's actually close to SF and worth every minute you spend there. Yosemite is however too far for a day trip.
If you want to go to Alcatraz, you must book far ahead. We've been to SF three times and never made the boat to Alcatraz. I hear the tour is worth the time.
That iconic view of Golden Gate bridge from Vertigo is from Fort Point National Historic Site, easy to find on google maps.
Don't fall off the trolley car.