Some of my favorites:
Parque de las Aguas... a really nice park that brings the community together. Even though they charge to enter, it's innexpensive and definitely worth it. You see entire families there.
Malecon de Miraflores... it's hard to imagine, but 20 years ago, these spaces were terrible. Now they are a tourist attraction and they have certainly added a lot of value to the apartments that overlook them.
Parque Reducto #5... a solemn place, since it was a battle ground and there is a cript under the flagpole, but its a tranquil place for a picnic, and you can often see people doing Tai Chi in the park. There is a small site museum there that details the war with chile in 1879. There is also an old locomotive that the kids love to climb around.
Parque de las Tradiciones (on Ricardo Palma), this park is in the middle of a busy street, but what I love about it is the way they have created small hills (about one meter high) which greatly reduce the sound of traffic. A great design.
But yeah, Lima could use some more public green spaces. Good for families, good for peace of mind...
It would be great if one day a part of the air force base in Surco (which is huge) could be turned into a park. Also, the area around the hipodromo is mostly unused, but belongs to the Jockey club. That would be brilliant to have a public park there.
"Hay que distanciarnos hoy para luego abrazarnos más fuerte".
-Guiseppe Conte, primer ministro italiano.