Perspective of where things are.
As well as getting good road maps, you might like to get a wall sized map of the USA. Put it where you see it every day, and you will soon get a very good idea of what is where, and the relationship of cities and attractions to each other. I see mine every morning when I wake up.
Lifey
An outline to help get you started.
As has been said, completing a loop would work well for the list of attractions you want to visit and that way you can see which of the 3 city's offer the best value flights. Your personal choices are the only ones that matter and those at the moment have you spending 10 days in 3 citys including the flight to NY leaving you 10/11 days for your trip. Wherever you start from I would plan it so that you are heading south down the coast between SF and LA as that will put the Ocean on your side of the road. I would certainly recommend you travel the coast highway, but CA1 is slower going so you will need at least 1 overnight stop and might enjoy 2. As well as the natural wonder you might enjoy Monterey and Hearst castle near San Simeon. From LA you would first go to the Grand canyon, which you could do in one day, or you might like to break the journey. Two nights and a day and a half is a nice amount of time at the canyon [south rim] and then you could head to Vegas. After your time in Vegas you could take a drive across the wonderful landscape of Death valley and stop in one of the towns on US395. DV will be very hot but can be enjoyed from the car with short stops, but carry water and sun protection. From US395 you would enter Yosemite via the Tioga Pass [CA120] that crosses the mountains, an amazing drive and should allow plenty of time to have a stroll and enjoy the views. I would recommend at least 2 nights and possibly 3, it's a wonderful place. That leaves you a bit of time over where from Yosemite you could head to Sequoia NP, or north of San Francisco to [Napa valley, Muir woods, Point Reyes] and drive over the Golden Gate bridge. If you done this, before heading over the bridge you could drive up the Marin Headlands on Conzelman road for spectacular views of the Bay area, bridge and City. If we rewind a bit, instead you could instead consider leaving GC to the east and visit Monument valley and then drive through Page AZ to Zion NP before heading to Vegas. You have a good link in the first reply and once you have studied the maps and researched and decide how to go about it, we can help piece together your trip together.