Miraflores and San Isidro are both lovely neighborhoods. One of my clearer memories of Lima is the taxi support system. There are tire changing stations seemingly on every other corner. When you get a flat, the taxi pulls in, and --whoosh!-- five minutes late, the replacement tire is on the car and your journey continues. A very efficient system for their needs.
The Inca market in/near Miraflores is worth a visit if you haven't had a chance to stop at the Pisac market in the Sacred Valley or spend much time in Cuzco looking at the handicrafts. Some of the best sweater selections are actually at the airport. If you're looking solely for good buys, there's a co-op that does handmade sweaters in a couple of shops in Cuzco. I didn't specifically look for them in Lima at the Inca market. The label is Artesanias Illary from Cusco. If you are buying the handmade sweaters, look at them very carefully and don't buy unless you try it on. Make sure the sleeves are equal length, the pattern is regular, the size holds true throughout the garment, etc. We had to fish through about 4 sweaters before we found one without obvious sizing problems. I love it and still wear it many years later.
The Gold Museum is a bit controversial locally (don't remember why anymore) and, of course, the sex museum is a must-see. We also came across the changing of the guard at the President's Palace. It was mobbed by local school children all wearing uniforms - in this case, track suits. The uniforms are quite ornate. The design dates back to the early 1800s.
Lima gets about 4 inches of rain per year, so it's often hazy from the dust in the air.
My 'ah hah' shopping moment was finding Carlos Chaquiras silver works in Cusco. I learned later he's considered one of the best, if not the best, silversmith in Peru. I don't know if his work is available in Lima, but ask the concierge. I find it remarkable and enjoy wearing it. My only regret was not buying one of his icon statues when I visited several years ago. Here's the link:
http://www.carloschaquiras.com/ Enjoy! Anne