The "luxury" bus we boarded at the border came with an extremely serious (and nutty) travel attendant who ushered us quickly onto the bus. She decided that it was her job to keep anyone from exiting the bus at any time. This was a huge pain, because we hadn't purchased a lot of water, knowing that we would be able to buy some en route. We decided that this was not a customary procedure, as most of the passengers were getting angry and began hurling out insults directed at our hostess. This caused the utterly crazy woman to become increasingly militant until she was waging a full out war on her unruly passengers. One of the few Western tourists on the bus had to leave us quite early on, the attendant had told her that the bus bathroom was only for peeing, but was not letting her exit the bus to use other facilities!? The poor girl looked utterly distressed as we left her in some town. When we exited the bus in Lima it was the first breath of non-recycled bus air we had taken in over a day, we were excruciatingly thirsty and completely exhausted. Lima is a sprawling, confusing city. We were relegated to the rich tourist district of Miraflores by lack of creativity and adventurousness. With only two days in Lima, without even a map or guidebook, we didn't plan to do much (we were only in Lima because it saved us money on the plane tickets). We visited the amazing sights of Miraflores: (1) Two blocks of giant tourist souvenir warehouses (highly recommended by the adorable American couple we met) (2) The modern ocean-side shopping mall (where Yann bought a small Dunkin' Donuts coffee). Despite the riveting excitement of Miraflores, we had our fill of llama trinkets and pashmina shawls and wanted to see other neighborhoods of Lima.
On the advice of our hostel staff we took a taxi to the historic downtown centre of Lima, rather than take public transportation "which would require transferring buses in a bad neighborhood". We were skeptical about all the warnings, but we had no guidebook, and the only map we had was a small tourist pamphlet. Since most of Lima's sights are concentrated within a few blocks, we knew once we were downtown, we didn't have much searching to do. Our taxi driver dropped us off at the Plaza Mayor in time for us to watch the bizarre changing of the guards ceremony. Bizarre, because spectators have to watch it from outside the gates of the Presidential Palace, actually from across the street. Crowds of school children, families and tourists jostle for position on the sidewalk, across the streets from the gates of the palace. To make sure no one gets to close, a row of riot cop stands between the crowd and the palace. I watched the routine while Yann was entertained by a grumpy old Peruvian man, who spent 20 minutes pointing out all the similarities between the French, Italian and Spanish language.
After the excitement of the changing of the guards was over, we wandered around the Plaza searching for something to visit. We walked along a pedestrianized street until we were behind the Presidential Palace facing the Rimac river and a large hill in the distance dotted with brightly-painted homes. We decided to cross the river to get a closer view. 
As we crossed the bridge, we noticed the lovely colonial architecture and a large church in the street directly in front of us. We strolled down the street heading towards the church, carrying our large day bags, and our even larger cameras hanging around our necks. We left the majority of the palace riot police standing on the bridge behind us. We could still spot the fluorescent yellow reflectors of the single police officers stationed at every street corner in the distance, so it didn't feel like we were leaving the tourist district. I remember making two brilliant observations as we walked along; "Boy! people sure like to whistle around here!" and "Boy! That's the third person who passed us making the sign of the cross!". Yann made the third astounding observation "Look, those people across the street seem to be waving at us!". Once we concluded that the shopkeepers had in fact leaped out of their stores to wave us down, we stopped to analyze the complex flow of information coming to us in the form of subtle clues. At the same time, we bumped into the last visible policeman stationed on the street. 
The kind shopkeepers were looking out for us, and were in fact desperately waving their arms and pointing towards the Presidential Palace. The policeman, after instructing us to hide our cameras, stood in the middle of the sidewalk blocking us from moving forward. The policeman kept repeating "peligroso", which neither Yann nor I knew the meaning of (so much for our "Speak in a Week" Spanish CDs). It took us a surprisingly long time to decide that we should in fact head back towards the plaza. We were actually pretty frazzled and we sped back from where we came from, to the sound of the same whistling, now taking on a new and slightly more alarming meaning. Oh, and we looked up "peligroso" in our pocket dictionary once we were back in tourist territory: "dangerous". Thus ended our Lima exploring, we were both mad at ourselves for our bad judgment and we concluded that such naive travelers could only be set loose on Miraflores, which is where we stayed for the rest of our time in Lima.
Note: Back in Canada, we came across a blog describing a traveler's day in this same neighborhood (Cerro San Cristobal), where he explored the homes on the mountainside, met locals and had no problems whatsoever...