¡¡Hola Gerry!!
Well, glad that you are moving to Lima. Currently I do not live in Lima but a buddy of mine, Luisefe does.
I have surfed and dived in the beaches of the bay Lima, but that was quite a while ago - when I was a kid. And even were able to find flounders near the Regatas Club.
There is a strong community of spearfishermen in Lima and a Federación Naútica.
There are beach towns starting at the edge of the city and going basically continously south all the way to 200 km (125 mi) . So you can hang in there in the summer months.
Among some close places around Lima where people scuba or spearfish are Isla San Lorenzo, Pucusana, Ancon (north of Lima).
About 3 hours from Lima you have Paracas, a national reserve park with its own bay and with sea lions, the guano islands, a posh hotel (Paracas hotel), small rays everywhere and incredible fauna and flora. And also you get to see the preincan cultures of Paracas and Nazca (the one of the lines and draaings you can only see from a plane in the middle of the desert). I have scuba in paracas but that is a place that I would love to go.
And in the northern part of the country you have Punta Sal where you can even go for big game fish. Warmer waters since the Humboldt current leaves the coast and it is an incredible and amazing place to be.
Regards,
Guillermo.
PS: El Pisco es Peruano. jajajaja , no me pude resistir.