Hey,
Peru is a very nice place to visit. You can spend one month in Peru visiting the most beautiful places of this country. You have the option to know the coast, the highlands and the amazon in one country.
If you will start in Lima, you can do a great circuit.
Starting in Lima you can take a bus to the Natural Reserve of Paracas, at Ica city. There you have the option to do Ballestas Island tour where you will be able to observe Southern Fur Seals, Sea Lions, different types of boobies, pelicans, Humboldt penguins and other sea birds. Also, driving 45 minutes you have the option to overflight the Nazca lines from Ica.
It is recommended to stay one night there and take the bus to Arequipa next day.
Arequipa is a Colonial city, it has a very nice architecture, its old houses are builded with a volcanic stone. You can take one day to visit and know the city. The Colca Canyon is located 4 hours from Arequipa. It is one of the deepest canyons of the world. Also you can have the opportunity to see the Condor flight and enjoy the culture of this area. I suggested to stay 3 days.
You can continue your trip to Puno, there are touristic buses which drive from Colca. At Puno you must to know the Titicaca Lake and if you are searching a vivencial tour, you can stay one night at Amantaní Island. This tours can take you 4 days sleeping at the lake.
The 4th day you can take the bus or train to Cusco. As Jabe suggested you, take some days to visit the city and acclimatise. It is true, you will need to take a tour to the Inca Trail cause you need a permit. There are a limit to this tours and have to book it in advance.
In Cusco you must to visit the city, the Sacred Valley, obviously Machu Picchu and if you have more time the south zone. There are the most visited places on this city, however, there are another places but not least important that you can visit as Choquequirao or Salkantay, there are trails a little more difficult than Inca Trail. Also, if you like the adventure, you can visit the Action Valley.
If you would like to introduce to the jungle, maybe you can visit Manu, there are many tours according your expectations.
Also, you can flight to Iquitos and browse the Amazonas. There are tour to Pacaya Samiria Reserve or tours more simple.
If you have any question, please, don't hesitate to contact me. I visited many places in Peru.
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