Budget mid range
Yes it can be doable a non hectic way if you managed to do it from the right start.
You'd better start from the north of Morocco. Start from Tangier down to Marrakech passing by Chefchaouen and Fes, and from Fes to the desert then head to Marrakech through the Atlas Mountains. if you did not do it this way you will have to have duplicated location visit.
And if it's your first time visiting Morocco, i do not recommend to hire a car,
you may find it a bit difficult to drive here, especially in the crowded Marrakech. you'd better go with a Moroccan travel agency. a travel agency can design a beautiful itinerary for you that fit your budget. You'd better avoid a group tour, a Private Morocco desert tour is more enjoyable. Recommend a 4x4 land cruiser with A/C 'cos it can be hot in the desert.
Enjoy your Tour
I think it is definitely doable, but it would be a little too rush for myself personally. If you can rent a car for part of the trip I highly recommend it.
When I was there we (my partner and I) flew into Marrakech and stayed in a riad for a few days, then picked up a rental car at the airport. Driving was a little stressful getting out of Marrakech, but actually wasn't as bad as I thought, and after that was really easy. The roads are in good condition and the traffic wasn't bad at all.
We decided to drive on a dirt road to see Telouet. It was easy even in our small car. We just had to drive slow. We also saw Aït Benhaddou, Ouarzazate, Er-Rich, and Azrou before returning the car at the Fez airport. We spent a few days in Fez before flying out.
Driving does offer a lot of freedom, but I know it's not an option for everyone. Buses are pretty easy to use and are the cheapest way to get to the places on your list. Trains are an option as well.
If I went back to Morocco I would probably do one of the overnight camel trips into the desert. You can organize those before your trip or at a travel agency in a city once you arrive.
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