If you travel during Easter (Semana Santa), you won't have any problems finding “festivals/events worth attending” Once you are in Peru, talk to the hotel staff, they'll have plenty of suggestions for you.
I traveled to Peru in 2010 and I was there October-September. Here are my suggestions.
I haven't spend much time here, but I prefer to stay in the Miraflores district. This is one of the upscale sections of the city. You'll be close to the beach and surrounded by bars, restaurants, stores, art galleries, etc. The Barranco district is also along the Pacific and a cool place to hang out.
If you plan to visit Machu Picchu, you'll have to travel to Ollantaytambo to catch the train to Aguascalientes. But don't just pass through Ollantaytambo, checkout the ruins and the countryside.
The city center is small but has interesting churches and monasteries. The night tour of the Monasterio de Santa Catalina is supposed to be very popular. I thought the entrance fee was kind of steep, so I skipped the monastery and instead went to a bar. If you are a foodie, ask locals to tell you about their favorite picanterias (restaurants that serve home-style spicy food). From here you can take a trip to the Colca Canyon (supposedly deeper than the Grand Canyon) and stay with a local family in one of the small towns of the Colca Valley. If you are the adventurous type, skip Colca and go to the Cotahuasi Canyon (deepest canyon in the world!), you'll need at least 5 days. Oh, if you are in really good physical shape, try to to summit the volcano El Misti. The flight from Lima to Arequipa is about 90 minutes. Taca (www.taca.com) flights are cheaper than LAN's (lan.com). I paid a little over $100 for a one-way ticket in September.
If you are the outdoorsy type, go to Huaraz. This is the gateway to the Cordillera Blanca, which is just beautiful. Since you speak Spanish, you might enjoy living with Andean farmers in the small community of Humacchuco (right outside the Huascaran National Park). They offer basic, but clean and colorful rooms, day hikes, and delicious home-cooked meals. I stayed in this community back in September. I would stay here for at least three days. LCPeru (www.lcperu.pe) has flights from Lima to Huaraz for about $99 each way. The flight takes only one hour. You'll get an awesome view of the Cordillera Blanca. The trip by bus is about 8 hours.
I did not feel the need to rent a car. I got around just fine using taxis, minibuses, public buses, rickshaws, and even tourist minivans. You can travel with a tour group and just pay for the transportation. This option is usually faster and more reliable than public transportation. Outside of Lima, you can hire a driver for a reasonable amount.
Here are some pictures from my trips.
Have a great trip!