Yes.
My trip to Peru in June-July this year was: arrived in Lima before 9pm, 2 nights in lima, bus to Nazca, a night in nazca. Marcos who works at hostal camiluz where i stayed is also a tour guide, he gave me a tour of 3 sites but it he charges 400 soles, probably per person. Then overnight bus to Arequipa but I had trouble sleeping on the bus. Your experience might be better. One night in arequipa, overnight bus to Cusco, taxi to Ollantaytambo, 2 nights in there, day trip to Machu Picchu, taxi back to Cusco, 3 nights in Cusco, plane to Lima, 4 nights in Lima. There is no such thing as the perfect itinerary. Check the Rough Guide and/or Lonely Planet guidebooks.
Most travelers pick just a few museums and skip the rest. A lot of travelers skip most of the museums in Lima. You will see some good objects in some museums, and after seeing multiple art and archaeology museums, I noticed very similar objects in more than one of the museums was in. Unfortunately, I got a disease in lima that affected my digestive tract and I stayed in my hostel for most of a day. I ended up with only 2-1/4 whole days for museums in Lima. 7 whole days in Lime and another 7 in Cusco is too many in either, for most travelers, unless you are taking day trips, but do not attempt to do a day trip from Lima to Nasca.
There are 5 commercial airports in Peru. For everywhere else you should take the bus, or a taxi if the cost and distance are low enough. Traffic in Lima, Cusco, and Arequipa is too crazy to rent a car and then who knows how much time you would waste finding parking spaces. Don't try to see Machu Picchu as a day trip from Cusco, if you see it. Or investgate traveling to the sites in Northern Peru that few Americans go to - Chan Chan ruins, the city of Trujillo, and so on. I took a few short rides with Uber and reserved some taxi tours with Taxidatum.