"Finding Nirvana is like Locating Silence" Jack Kerouac- Dharma Bums
This picture here pretty much sums up Lima. All of these cars are trying to merge onto a one way one lane road from a normal two lane bi directional road. So not only are they all going at once, but all of the cars in the foreground on on the wrong side of the road. This is common place as well as motorcycles on sidewalks so keep your head on a swivel.
This picture was taken from a double decker bus that took over an hour to go 6km.
Our suggestion would be to pick a neighborhood a day to explore to minimize time spent in traffic.
ProTip: Taxi's don't have meters in Peru. This means two things: 1) There are a lot of people pretending to be a licensed taxi, which can be dangerous for you. Only take yellow cabs or have your hotel call a company they trust. 2) All fares should be negotiated before getting in. These guys can be aggressive and often demand extra tip money.
The Presidential Palace in the Plaza de Armas was definitely a cool place to check out. We hopped onto a double decker tour bus to get us from Miraflores to the plaza. With the tour we only had an hour here but you could very well spend at least half a day exploring this area. Don't be put off by the riot police. Apparently they are there all the time, just in case of demonstrations. Remember, this building is the equivalent to the White House, and you can get much closer to it, so the extra precaution makes sense.
The Cathedral of Lima. Definitely worth checking out. We went for a bit but then were shoo-ed out by a very kind monk because I was wearing shorts. If you plan on visiting ladies, have your shoulders covered and wear a long skirt (covering your knees) or pants.
We did tour the Franciscan Museum/church and it's catacombs. You are not allowed to take pictures inside but there is some very ornate wood work, and the library is not to be missed. Monks still live in this particular monastery so some parts are off limits. Here it was believed that the fastest way to heaven was to be buried underneath the church. For this reason, even the common towns folk were buried in the catacombs.
Overall, there are so many remote and amazing sites around the country that Lima is not a place I would spend a lot of time....