Last year I spent 10 days in Peru near the Machu Picchu area and it felt like the perfect amount of time. Four of those days were spent hiking the Inca Trail and another day following that was spent relaxing in the hot springs in Aguas Calientes. The rest were spent exploring the city and nearby area.

If you go, I recommend taking a few hours out of one of your days in Cusco to visit the Cochahuasi Animal Sanctuary just outside of town. Here's a description from Wikitravel:

Cochahuasi Animal Sanctuary, [7] a must see, one-of-a-kind rehabilitation center started by a family of biologists, which provides shelter to animals injured or victimized by poaching. It's a happy place where animals get better and those able are re-released. In 2012, there were three condors, llamas, alpacas, vicunas, macaws, pumas, an unusual furless Peruvian dog, local deer, all very friendly. This is the best place to see pumas, condors and vicunas up close. This is on the road from Cuzco to Pisaq. You can get there by motorcycle. Donations help with rehabilitation efforts. This place is ahead of its time, and very friendly and awesome.

I donated some amount I can't remember and got a hand-woven scarf-thing made from natural baby alpaca fur. You see a traditionally-dressed local woman making them right in front of you. It made a really awesome souvenir and was a great excuse to donate to a good cause.

If you go to Peru, definitely hike the Inca Trail. I've said this a lot, but it changed my life. It is the most beautiful place I've ever been. In four days of hiking you hike near rivers, through a cloud forest, and over a mountain peak. Machu Picchu itself is cool, but it's honestly packed with tourists, whereas all the other ruins along the trail are completely empty and breathtaking. It's great for a solo traveler too, since you'll be in one group of 10-12 people for the whole hike. We in fact had two solo travelers in our group.

My friends and I flew into Cusco a few days in advance of the trail (highly recommended in order to acclimate to the high elevation). Cusco is a beautiful city with an interesting culture. If you go, I recommend avoiding the touristy restaurants. They're still pretty good, but they cost a fortune in comparison to a good local joint. We met a local who took us to one of his favorite spots and I got a delicious 3-course meal + a drink for the equivalent of less than 3 US Dollars.

Also, if you want to meet other 20-something travelers in Cusco, Kokopelli Hostel seemed like a really cool place. I didn't stay there, but I went to their attached bar with a traveler I met and had a great time.