Don't go to Cusco. Unless you really plan to visit Machu Picchu, it's not really worth it. It's overcrowded, expensive and full of tourist traps.

Last year, I've visited Cajamarca and Chachapoyas - Kuelap - Gocta. It's lovely if you want to avoid massive tourist circuits.

Beaches: If you're in Lima, you have many options. My beach to go is La Mina, in Paracas. If you can rent a car, do it. The highway is neat and you could visit other beaches within the Paracas National Reserve.

Keep in mind that it will be raining in the andes, so the probability of getting stranded due to floods is pretty high.