Hello,
I did a similar trip in the New Year.
We wanted to see the jungle so we did as below:
Lima
Lima - Iquitos
Iquitos 4 days
Iquitos to Cusco
Cusco and around for 3 days including train to MP
Train from Cusco to Puno but just for the overnight and then flew to Lima
4 days in Lima including an overnight trip to Paracas.
If I could do it over I would do as follow:
Lima
fly to Cusco
Cusco, Sacred Valley Machu Picchu
Train or tourist bus to Puno
Lake Titicaca
overnight bus Puno to Arequipa
Arequipa and Colca Canyon
fly Arequipa to Lima
Or you can do it in reverse and fly to Arequipa at the start. You have time for all these places in 13 days.
For surfing and relaxing, there are good waves in the south of Lima, you can sleep over in Paracas and do the Ica excursion too.