As strange as it seems from May to September, there is no sunshine in Lima. If you imagine an overcast day that lasts for five months, then you are getting close to imagining it. Therefore, it is necessary to get out and find some direct sunlight. One of the places is Paracas, three or so islands to the south of Lima. Go for a weekend. There is a national park and sunlight. Maybe. If you really want to make sure, go down to Ica, location of the Nazca lines. Make sure to stop at the pitstop at marker 52 for breakfast.
We went for a weekend. Paracas is a small town that seems to exist nowadays for the tourism related to the Paracas National Reserve, a vast sandy national park, and the Ballestas Islands which is part of the park but a separate boat tour. These islands were the source of guano, bird poo, which is used for many products, including fertilizer. It was a big industry. The birds still produce and they like to aim for the tourists (wear a hat and long sleeves). You will also see sea lions sunbathing. The boat ride is two hours with no toilet, no roof, and lots of wind and water. Be prepared.
As much as I enjoyed the boat ride and watching the local fauna (a man and his 12 offspring) on the boat, I actually preferred driving around the desert part of the reserve and finding well appointed viewing platforms and amenities along the way.