You've got several places where you've allotted more days for the drive than you'd really need. You

day 1-7 Drive to Bozeman MT pick up my friend at the airport, I was thinking of going via Lewiston to see bits of the Lewis and Clark trail but what would you recommend? 7 days for what would be a 12-14 hour continuous drive should allow for some side trips.
after that we plan to fly to DC early in the morning, take a train to New York in the afternoon the next day and my friend would leave 2 days later in the evening while I would stay an extra 3-4 days, maybe go see Boston.
The only serious red flag I see is the rim to rim hike in a day. Attempting such a feat is probably the biggest reason for calls for rescue at the Grand Canyon. Unless your fair bit of hiking includes things hawaii rental car like hiking to the top of Mt. Whitney or a similar hike that would be considered one of the most extreme hikes on the planet, don't even think about.
Otherwise, you might want to think about more time in the National Parks. Most of them it looks like you've got less than a day planned. hawaii rental car Yellowstone in particular is a place where you should plan to spend at least a couple of days. It looks like you've got plenty of time to work with.
The idea for transportation is for me to fly to Vancouver (from Switzerland) train down to Portland via Seattle and then rent a car for the 71 days to Chicago, fly to DC train to NY and then fly home. Flights should cost approximately $1500 each and renting a car and fuel should cost about $7000-$7500 hawaii rental car total because we are both 22.
In total we are expecting to spend about $22,000 (not each) with me spending a bit more and him a bit less because my trip will be slightly longer. Does this seem about right or are we underestimating the costs?
By in shape I mean that we can both run above 2 miles on a Cooper test (12 minutes) and he has recently done military service (which is compulsory here for some crazy reason) and I am currently training for mine which starts in October. I know a hike here which is 12 miles and has about half a mile up and then the same down which is about half of the GC rim to rim in all aspects. hawaii rental car I'll see how long it takes to do that twice and if it takes less than 8 hours without being to strenuous it should be ok to add an extra 6 hours for the heat, start at 5am finish at 7pm.
When you say we have plenty of time to work with what do you mean? do you think we should be driving more the days we are driving or do you think we are spending hawaii rental car too long in some places? I thought Yellowstone would be worth 2 days but wasn't sure what to take out. Moab looks incredible, would love to spend some time there!
You've got several places where you've allotted more days for the drive than you'd really need. You could easily get to Bozeman in 2 days, and you're planning 7. That's not a bad thing, hawaii rental car but its an example of an area where you could easily take less time.
I know a hike here which is 12 miles and has about half a mile up and then the same down which is about half of the GC rim to rim in all aspects. I'll see how long it takes to do that twice and if it takes less than 8 hours without being to strenuous it should be ok to add an extra 6 hours for the heat, start at 5am finish at 7pm.
I can't begin to stress how bad of an idea that is. The Grand Canyon really can't be compared to any typical hike. A typical hike is hardest at the start, and is easiest at the end, as you go back down hill - the Grand Canyon is at its worst, when you are the most tired. hawaii rental car The heat and desert air also saps your strength.
Again, hawaii rental car there is a reason the National Parks Service strongly discourages anyone from attempting to hike to the rim and back in a day. It very frequently puts them in the dangerous position of having to rescue such foolish souls. If you regularly scaled 14,000 foot peaks or were in some other ways an extreme athlete, then go ahead, but unless your military training qualifies you for special forces, this is far more than basic training or an afternoon hike would prepare you for. I'll also say that I think you're seriously underestimating the hike if you think you'll want to hike back again, going rim to rim twice in less than a week!
It puzzles me why you are allotting three weeks to retracing route 66 - of which not much remains. This is a drive which can be done in four days. Maybe add as many days to search where the sections still in place, are.
If you are looking to take days from anywhere, it is where you could well do with fewer. Places where I would add more time would be in the large National Parks - Yellowstone, Yosemite and Grand Canyon. Especially if you are into hiking, of which there is plenty. You might also like to do a little more research for your rim to rim hike. I fear you may be underestimating it.
My brother was an amazing athlete who thought he could hike to the bottom of the GC and back up in a day. He found out the HARD WAY that it was a 3 day trip: one day down, and then TWO returning. The three guys with him almost didn't make it back up. All four were great athletes in great shape. DO NOT attempt to go rim to rim in one day.
The Million dollar Highway is quite spectacular and although most of Colorado is too, it's the route I would take. You could head down through Leadville to US50 and then head over Monarch pass, through Currecanti Nat Recreation area and Black Canyon hawaii rental car of the Gunnison NP. Alternatively, you could head towards Colorado Springs from Denver hawaii rental car [Garden of the Gods, Cave of the Winds, Pikes Peak] and then head towards Pagosa Springs [Hot springs resort] and Durango on 160, perhaps visiting the Great sand dunes NP on route and then head North on the 'MDH'. You then have the option of driving the complete 'San Juan Skyway' [of which MDH is part of] and travelling to Telluride and Dolores where you could end up at Mesa Verde NP, or continue north to Grand junction [Colorado National Monument] and then head for Moab and Arches/Canyonlands as suggested by Michael.
I have to agree with the others regarding the rim hike, you would need to camp in the canyon really or stay at the Ranch. There is no need to pay $85 for a bus though, you could simply drive to the south rim from Monument valley and stay a night before continuing to Page and the North rim and hike as far as you feel comfortable with from either rim, or stay a night at the bottom. It looks as though you have 4 days to hike both directions alloted, so you could take 2 days each way, but it's still a lot of hiking and it can get real hot in the canyon.
I would not drive all the way to Cedar City to visit Zion NP. Springdale UT is a wonderful little town and is right by the entrance to the park. You can actually get on the free shuttle bus from town and not have to move the car. I would recommend at least a full day at Zion, it's a wonderful hawaii rental car park ! As you sound quite adventurous, you will find many amazing hikes here and you might want to check out hiking in the Virgin river through 'The Narrows'. You should also consider Bryce canyon !
I don't think you will find lodgings in Rachel, there is not much there other than the Little'Ale'Inn where you can eat and drink and look at 'out of this world' photography. I think the nearest lodgings hawaii rental car would be Alamo. As much as I love a drive through the desert I'm not sure if adding a whole day driving around the desert is worthwhile. You could get to Alamo[?] via Rachel same day from Springdale and then continue on to Vegas. If you went via Cedar City you could take a short detour to Cathedral hawaii rental car Gorge State park between Pioche and the Lincoln county Airport. Of course you could just head down I15 and visit Valley of Fire State Park and get your desert 'fix' in Death valley.
I would do days 33 through 37 slightly differently. You are in Death valley after a couple of hours from Vegas so you can explore quite a bit that day. Remember it is extremely hot and you will be limited with time from the car, even though it's still well worth it. The next day [34] I would continue exploring DV as I made my way to the Bishop CA area. Day 35 continue to Yosemite hawaii rental car and spend a lot of the day on Tioga Pass [CA120] giving me day 36 to explore Yosemite valley and 37 to visit Glacier point and Mariposa Grove areas of Yosemite, it's an amazing place with lots of hikes/walks !
I would have to agree with Lifey about following hawaii rental car 66 to Chicago. There is nothing wrong with that and you will find plenty hawaii rental car to do along the way, but you could cut that back to 10-12 days and have more time in other places along the way, quite a few of them already mentioned above. Having got this far reading your post, this would actually be a good time to visit the south rim of the Grand canyon. On the way to Chicago you could also visit, Sunset Crater, Petrified forest, Canyon De Chelly, sleep in a Wigwam in Holbrook, visit Caddilac Ranch near Amarillo and spend a little time in Albuquerque, Santa Fe and St Louis.
Unfortunately I can't pick up my friend from Bozeman any earlier than on that day as he could potentially have exams until the previous day. This means the reshuffling has to come from after that point as the next time I could pick him up would be in Denver hawaii rental car and it would be a shame for him to miss out on Yellowstone and Grand Teton.
Grand Canyon: Though I think we'd be ok I understand there's a reason for all the warnings. If we ask for a permit which is 2 nights at Bright angels Campground having started from the North, this is a long hike but all downhill. If when we arrive there it's not even mid-day and we're feeling fresh we'll keep going if we're knackered we'll make camp. On the Second day we'll either walk down to Bright Angel if we made the 1 day hike or go for a day hike as far up on the south side as we think we can manage hawaii rental car if we didn't. On the 3rd day we'll go to Cottonwood camp and then on the 4th day head back up to the north rim.
Changed hawaii rental car driving between Denver and Grand Canyon North Rim so that we have slightly less time in Monument Valley, drive more on driving days (nicer route shortest path) and have a f