I do similar types of trips a couple dozen times a year. Have a business meeting in some city, then go backpacking. Often I don’t have much time to plan, but can usually find a cool remote trip somewhere. Sometimes I have to be creative with stealth camping. At the same time I like to catch some historical and cultural stuff. Right now I am sitting in a hotel in Columbia, SC -- my planned trip not going to happen, roads are closed due to ice. Should have done more pre-work :)
The Grand Canyon is special. Luckily for me, I can drive there in a few hours. To fly there and deal with the logistics, I would set aside at least a 7 day trip. 14 days would be better. I mean, would you take your kids to Disneyland for 30 minutes?
So here are some not so conventional suggestions…
First read Two Years Before the Mast, by Richard Henry Dana.
Fly into LAX, Long Beach, or John Wayne airports.
Take a shuttle to Dana Point.
Stop by the visitor center, the Pilgrim Tall Ship (replica of the ship in Dana’s book), walk around the beach – it is awesome.
Take a 2 hour whale watching boat tour – this will be prime time. If you're inclined, rent a sea kayak instead.
Then take the Express boat to Catalina Island.
There are some Catalina Island trip reports posted here on BPL. Should be able to do a great 3 day hike. Spend the last night in Avalon Bay. Take the express boat back to Dana Point, San Pedro, or Long Beach. Take shuttle to airport.
If you go back to Dana Point and have time, hop over to the Mission at San Juan Capistrano… you need to research the history of the 21 Missions and the El Camino Real ahead of time to fully appreciate it.
Fly into Vegas.
Catch transportation to Boulder City (or Hoover Dam if possible). BC is close to the dam.
Take a tour of the dam. It is worth the time.
After the tour, you can walk across the dam into Arizona or go north through the railroad tunnels to Boulder Beach (Lake Mead). You can stitch together all kinds of trips in either direction, though it may be best to hitch a ride from Boulder Beach to the more remote areas to save some boring walking. There are a few trillion gallons of water in Lake Mead. So water is not a huge concern.
If you have a packraft, you could launch below the dam and float through Black Canyon to Lake Mojave. Check the launch permitting regulations. Pretty cool. Then you hike back. If you do the Nevada side, you have to deal with the Black Mtns; many are unimpressed with them, I find them enchanting. Can be very, very difficult. To read about them, try Colin Fletcher’s, Man From the Cave. Or you can hike back on the Arizona side. Again, no trails.
All the hiking in Nevada and Arizona will need to be mostly cross country. Here are some samples
Lake Mead Walk-abouts
Highly recommended. They can provide you so many alternatives. Away from metro areas, public transportation limits your options. Rental car at airports are most expensive. Daily rates are higher and there are all sorts of airport franchise fees and taxes. Mid size cars are the cheapest, compact cars are expensive. Don’t purchase the fuel option. Don’t purchase insurance, your personal auto insurance probably covers the rental. Many credit card companies provide insurance if you rent using their card. Most rental cars have unlimited mileage. Some (few) don’t allow you to cross state lines. Of the large chains, National is usually the cheapest. Hertz provides the best service. If you take your rental car on dirt roads, wash it before returning it. I always rent a car on my wanderings away from home when I fly.
Edited to fix hyperlinks.