I spent 10 nights at Amankora last October, and thought it was one of the top 5 hotel experiences of my life. I went to all 5 lodges, and agree with the other posters that to see all 5, you must have the stomach for very, very long drives.
What we found most amazing about was simply that Aman could pull off such world class service, spa treatments, and (often) delicious food in such difficult-to-traverse environs. The rooms in the 5 lodges don't vary much from lodge to lodge--there are two room types in total: one type at 3 of the lodges, the other type at 2. But the exteriors, and the common spaces, are each very individualized to the locale.
Basically, you are not driving very far at all, as the crow flies, but because Bhutan is a series of north-to-south valleys, each divided by very tall mountain ranges, you spend hours switchbacking up one side of the range, and down the other, in order to get from one lodge to the next. What's more, to get to the lodge furthest east, Bumthang, you must traverse two valleys, because Aman hasn't yet built a lodge on the property they've apparently acquired in Trongsa, the valley separating Bumthang valley from the Gangtey lodge.
I grew up in the Rockies, but have lived in NYC for more than a decade, and I did get a touch of altitude sickness after mountain biking in Gangtey, the only lodge that is at a significant elevation. And another guest there had to be moved early to a different lodge because he also developed altitude sickness there. But we were the only two that seemed to be struggling with that at Gangtey.
So some quick reactions to the journey, the lodges, and activities at them:

DRUK AIR: Yes, if you can get a seat on the left side of the plane (left as you face forward), and the weather cooperates, you can see the peak of Everest, and a string of other "highest peaks in the world," en route from Delhi-Kathmandu-Paro. They don't assign seats in advance, so far as I can tell, so when you check in at Delhi, get there early to request a seat on the left side of the plane--people are clearly aware of this, so those seats go fast. And it's definitely worth paying the few hundred extra dollars for business class seats on Druk Air.

PARO: After all that travel, I think you really want Paro to be your first stop, since it's just a 30-minute drive from the airport. That 30 minutes will give you a taste of what the roads are like in Bhutan, and can help you gear up for what's ahead. And the setting's very majestic--mountain peaks all around, with one of the great peaks of the Himalaya, Jomolhari, visible on clear days. And with Tiger's Nest just a short drive away, this is clearly the must-visit lodge.

To Gangtey from Paro is a very long drive, but with the most exquisite scenery of the trip in the long valleys heading up to Gangtey--rice paddies hanging off the mountain sides, incredibly verdant and lush vistas, yaks along the road in the higher elevation approaching Gangtey.

GANGTEY: very small and intimate lodge, with exquisite views across the valley. Nice nature walks in the valley, or mountain biking. Visits within homes of farmers, a historic monastery on a ridge, etc. A very special feel here, given how remote and quite it is; one of the nights, we were the only two people in the lodge, and were made to feel like royalty, with personally addressed dinner menus, etc. The best breakfast pastries of the trip. Not sure how much time to recommend here--but if you have to pick between Gangtey and Thimphu, I thought Gangtey was much more special.

From Gangtey, the longest of the drives--yet with spectacular scenery--to Bumthang: locals praying to rocks along the way in a form of pre-Buddhist worship; prayer flags everywhere on the hills; stupas. Bumthang lodge is, according to our guide, rarely visited; he hadn't taken anyone there for over 6 months. Terrific architecture, ridiculously good spa treatments, and the best food of the trip--in the most remote location. How on earth does Aman pull this off? Some important temples are in this area, and at one of them, we chanced upon the King of Bhutan and his two sisters, who were warm and friendly and dignified, introducing themselves to us and welcoming us to their country. All this said, it's hard to recommend the additional drive to Bumthang--I didn't feel we really saw anything there that we hadn't already experienced in other parts of Bhutan. I'm glad we went, since I really wanted to experience all of the lodges, and with some Dramamine, I did just fine on all the winding roads. But those drives are really grueling, so the real must sees, in my opinion, are Paro lodge and then . . .

PUNAKHA: the most exquisite of all the lodges, set in rice paddies, across a swinging bridge covered with prayer flags, with a wonderful outdoor dining courtyard with tremendous views. There are only a few rooms, so it's seen much more wear and tear than the other lodges; in fact, it was the only lodge that felt a bit run down. But it's really a must. The dzong in Punakha is the most gorgeous of them all.

Finally, we were underwhelmed by THIMPHU. There seemed less to do and see in that area, and the lodge lacks the grand views of Paro, the otherworldliness of Gangtey, and the gorgeous intimacy of Punankha. We'd planned our visit deliberately in October because we'd heard the weather was ideal then, and that there were many festivals. The weather was ok--but we never had an unobstructed view of the Himalayas from the tops of the mountain passes we drove over--too many clouds, and some rain. The guide felt that by far the best time to go was in the spring, when all the wild rhododendron are in bloom along the roads--they say it's unimaginably beautiful then, and better to have some rain in the spring, and all that beauty, than the possibly clearer days in the fall.

Re: the festivals. I'm an operagoer, so I think I have a reasonably long attention span, but I found the festivals to be excruciatingly dull; 10 minutes was plenty to get the idea. Everyone sits on the ground, outdoors, and it's hot and very, very dull--with dancers making very repetitive movements for very, very long stretches of time. Our guide took us up into the rafters of one of the temples, from which we looked down upon a private dance conducted by the monks, and it was truly a once-in-a-lifetime and thrilling experience . . . for about ten minutes. But the dances goes on for 2-3 hours, so we simply left when we tired of it--as everyone does. But I wouldn't let the festivals be the top driver of when you travel to Bhutan. It's nice to see for a few minutes, but a little went a long way. Outside the temple precinct, there more of a festive atmosphere, with lots of gambling going on, which we were welcomed to join, and thoroughly enjoyed. The people, everywhere, were wonderful.

I can't recommend Amankora highly enough. Uneven food, but much better than it seems possible to pull off--and the fact that they have five different menus (separate menus for each lodge) for each of breakfast, lunch, and dinner, in a country where most other foodstuff is cheese and chillies, is astounding. (Aman kills a yak each week for yak meat; there are one or two yak items on the menu, but otherwise they fly in steak and seafood and many other items from Bangkok each week.) Moreover, each lodge has a different welcome drink, all wonderful, tailored to the local environment--a sort of lemon and pomegranate tea in the warm and lush Punakha, versus a ginger drink to fight altitude sickness in Gangtey, etc. Different gifts left on your bed each night, dealing with a local aspect of Bhutanese culture. Different attire for the staff at each lodge, characterizing that area. An amazing, amazing place. And I would NEVER want to go to Bhutan without Aman--the food, the driving, the accommodations would all be very, very difficult, I'm afraid, otherwise.

This turned out much longer than I'd planned--sorry for the deluge.