Miraflores - you can easily do the hanggliding thing over the beach as it's from there
I'd go downtown to the city center / govt center and see the old churches (Francisco Pizarro is buried on the main square), including the one with the crypt and a gajillion bones geometrically arranged downthe road from the main square (I've already forgotten the name of it and I only got back a month ago - San Francisco?!?!). Any concierge or guide book can tell you.
If you dig it, get your nails done and a massage at super cheap rates (1hr massage - $20US including tip, nails $6US!).
Hit up the two Huaca archaeological sites right in the city. They predate Inca times are actually impressive considering the age and the fact that they're right in the middle of the city. Take a picnic lunch to El Bosque - olive groves as relax while people watching.
Eat lots of alpaca. Buy cheap alpaca sweaters / scarves for the fam back home. Pack toilet paper and hand sanitizer for the excursions around the city, and whatever you do, don't throw the tp in the toilet. Enjoy!