Like his namesake our own Jack Kerouac has apparently never been on the road that he is referring to.
I have driven up and down the snowy and icy switchbacks of US 89A that go from the floor of Oak Creek Canyon to the Scenic Overlook that's on the top of the Mogollon Rim literally dozens of times under winter conditions...and they will get the attention of even the most experienced of bad weather drivers
To your questions:
First of all rent the biggest car that you can get your hands on that has a V-6 and front wheel drive because on the long stretches of the West driver comfort becomes important as does the ability to safely make high speed passes on 2 lane roads >like US 89 & US 89A
Tucson to Sedona is a fairly easy trip with one major uphill climb up on I-17 going up Black Canyon and one major down climb from the top of the mesa heading down into Camp Verde
You can avoid running thru downtown Phoenix by taking the Loop 2002 exit off I-10 at Chandler
over to Loop 101 and then connecting that to I-17 N> get gas at the first I-17 exit and make a "pit stop " if need be
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Sedona to GCNP
btw the S.Rim of GCNP is at 7000'msl
This is the best way to do this trip .
Assuming that the switchbacks on 89A are open and that you feel safe about driving up them
then.. [If not then head back to I-17 and use that for your uphill ]
Take 89A to the Pulliam Airport turnoff
Get on I-17N
btw "I" means Interstate Highway and US Highways are what preceded them
take
I-40 E 2 exits
Take US 89 North to the Junction of SR 64 at Cameron AZ and make a left
Get gas in either Cameron or Grey Mountain which is 8 miles south
As long as you're in Cameron getting gas
This the best place for a pit stop and possibly lunch
http://www.camerontradingpost.com/
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Climb up SR 64 and when you see a sign that says "Entering Kaibab National Forest "pull over get out of your car and check out the view behind you because you can literally over 100 miles across the barren technicolor landscape of the Navajop and Hopi Reservations
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You will enter GCNP at the Desert View entrance
When I used to live an hour from the S.Rim Lipan Point was the place that we took all of our vistors to for their first view of the Canyon. and the reason was that unlike many other places on the S.Rim , in the view from Lipan and Desert View the River is clearly visible and in fact dominates the landscape below you.
What's also visible between Desert View and Grandview Points are almost all the rock groups that make up the Canyon including the GCN Supergroup
Anyway..
Drive on SR 64 stopping at everything that says "Point" on it>
Watch out for the mule deer ..and don't feed them
When you get to the "T" make a left to get to Tusayan or a right to get to the NPS Visitors Center,Grand Canyon Village and the rest of the hotels on or by the Rim.
Personally I would hold off making any hotel reservations beyond your Sedona dates and then call around just before you leave your hotel in Sedona to see what's available either in Tusayan or the Park or even the Cameron Trading Post
btw :"ya -ah -teh "means hello in Navajo
In a worst case scenario you could always find a place to stay in Flagstaff which has thousands of hotel /motel rooms available in every price range imaginable
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To Las Vega from GCN
From a weather perspective the trip has only one potentially bad spot in it ;the 20 miles from Williams to Ash Fork. Under heavy snow conditions the downhill trip in heavy truck traffic can get interesting at times
Once the world flattens out ,you're home free and it's an easy and boring trip to Las Vegas
Get gas at exit 48 and try to resist the urge to do 100mph..it's actually tough to do
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Just so you know :there is another stunningly lonely ,empty and beautiful way to get to 'Vegas
that takes you over the top of the Canyon
Weather permitting you may want to think about it
Pop this into mapquest exactly like this
GCN>Leees Ferry AZ>Mount Carmel Junction UT>Hurricane UT>LAS
Have a safe trip
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Update :
Help me out here: If you guys are on a budget then why are you using airport and car rental combinations that will easily add hundreds of dollars onto the cost of your vacation?
My experience tells me that if you fly into and out of major airport like LAS and you pick up and return your car to the same location it's just a lot cheaper.
Granted it's 400 mostly empty miles from Las Vegas to Tucson but if you don't hit too much Dam traffic or PHX traffic you can do it in under 8 hours ..something to think about
Me>Canyon hiker , former NoAZ resident [although the place never ever leaves you] and former NoAZ to PHX commuter