I'm sorry, but suggestions not to be alone at any time in Lima is IMO a bit extreme. But I do come from Guayaquil, which has a similar crime rate.

For me, I would travel alone but if you are really concern with the muggings in Lima, I suggest you stay within San Isidro and Miraflores.

Btw, don't travel in public transportation in Lima -that's dangerous..

The rest of Peru is ok.