Yes, I'd say it's safe. I met several girls travelling through Peru by themselves, too. There'll undoubtedly be some over-enthusiastic Peruvian men; but then, that's certainly not unique to Peru. Basic common sense should be all you need.
I wouldn't spend more than a day in Lima itself; the city is extremely boring, plus the smog and noise can be horrible.
Cuzco is the most touristy city in all of Peru, and you'll learn to hate everyone trying to sell you everything long before you have mastered the art of ignoring them. I don't know how you're planning on going there, but from the way you phrased that sentence, it almost sounds like you'd be wanting to head straight to Cuzco and then stay only in that area. That'd be a big shame; there's so much more to Peru. (Although I guess there's enough Inca sites between Cuzco and Machu Picchu to keep you entertained for an entire month, so maybe you just know exactly what you want to see.) 
Still, for alternatives, I can highly recommend Arequipa in the south (it makes a good halfway point between Lima and Cuzco, too, altitude-wise. Its 2350 meters are near-perfect for acclimatizing before you go higher up. Even better are some of the smaller villages in Peru, where you can explore the wondrous sensation of being left to your own devices without anyone trying to sell you something, and watch village-life go by at its own pace. I particularly enjoyed Caraz (north in the Cordillera Blanca; wonderful mountains if you want to do some hiking, though make sure you're well acclimatized before heading in that direction) and Cabanaconde (a popular base when visiting the Colca Canyon).
[ Edit: Edited on Nov 22, 2008, at 11:19 AM by Sander ]
