Check out the Archaeological and Anthropological Museum (Pueblo Libre) and La Museo de la Nacion. Avoid the Gold Museum, overpriced and boring. Stay in either downtown Miraflores, the new and modern neighbourhood (Macdonalds, Tourist Restaurants etc) or the old town, Plaza Mayor (not so safe at night), beautiful architecture, government palace, changing of the guard... from here you can also get a tourist bus to the top of a nearby mountain for great views over the city. Try Barrancas neighborhood in the evening for the bars. Lima also has some beaches - surfing, but never been.For a cheap market Polvo Azules, pirated Dvd's peso$3, cheap clothes etc...When you leave the airport and want a taxi haggle hard- to Miraflores the price is about S/.25 - 30, taxi drivers will try to charge us$ 25 - 30 !! three times as much.
I went to Lima about 4 years ago. Nice place. Much cleaner than Buenos Aires. Public spaces and squares are neat and well kept. Just for the record, I only visited the popular tourist spots and upscale barrios (e.g. Miraflores). I'm well aware that those places generally don't represent what a country is really like. But anyway, I think I can tell you one thing or two.
The Plaza de Armas is a must-see. There you'll find a lot of people begging for money and selling stuff. Some of them insist too much. It can get a little annoying.
In my opinion, the food was too spicy. I just couldn't get used to it but of course it all depends on your preferences.
Be careful with the drivers. They are even worse than here.
If you want to know anything else, feel free to ask. I'll be glad to help if I can.