Hi Shaina, there is an awesome place right in the middle of Lima called Huaca Pucllana and a day trip you can do to Pachacamac. From there I would probably head out to Cusco from where you can organise trips to Sacsayhuaman, Valle Sagrado, Ollantaytambo, Pisac (a personal favourite) and Chinchero. Obviously no trip would be complete without at least a day in Machu Picchu - I have heard a lot of people say it is too full of tourists etc etc, and quite frankly it is BUT for a reason. You would be crazy to visit Peru and not see it. I did the Inca Trail last year and it was incredible - lots of old jungle ruins on the way too but it may be too late for you to book depending on when you are going. The Salkantay Trail Peru is a worthy alternative though I haven't done it or there are short treks and day trips to Machu Picchu that you can book in Cusco.
There are a lot more I'm sure but these are the ones I have been to and they are all incredible! There is obviously a lot more to Peru as well if you have time to see it! Amazing country :)
In Lima itself, there are some huacas (temples). Huaca Pucllana in Miraflores is from the Lima culture (200AD-700AD) open Weds-Mon 9-5, lit up at night and has an on-site restaurant. Huaca San Borja from the Ichima culture in San Borja, also in San Borja is the Museo de la Nacion, Av Javier Prado Este 2465 - has great pre-Incan displays of artifacts, etc. If you are in San Borja, note the Surco River which runs down the length of most of the park there, is actually a pre-Inca irrigation canal. While in Lima go to the city and admire the cathedral, churches and visit the catacombs in the Convento de San Francisco (watch out for pigeons). Also the Inquisition Museum is interesting.
Up north in Trujillo there are heaps of sites - La Huaca del Sol and Huaca del Luna are 5k north-can get a taxi or bus-from Moche culture, Chan Chan-Chimu culture-5K NW,Arco Iris-4k from city-chimu culture, Huaca La Esmeralda 3 k-Chimu culture-usually has lots of the hairless dogs sitting around. Unsavoury neighbourhood so get taxi there and back-don't wander round there. El Brujo complex-60K north-Moche culture-can do a day tour there. Go out to Huanchaco - beach town and see the caballitos de totoros-the reed boats still made as in ancient times.
Go up to Huaca Rajada 35K NE-Moche culture, Tucume-21k-Sican culture, Batán Grande - 40K NE-Sican culture. Make sure you go to the Royal Tombs Museum of Sipán - 11k north of Chiclayo-wonderful museum. If you get to Casma about 170K south of Trujillo, go to Sechin Bajo - about 3500BC and may be the oldest building in the world. Also Chankillo worth seeing there.
Going to Cusco, a must do- lots to see in Sacred valley. You can do day tours or just hire a taxi to drive you around. Machu Picchu is a must - just be aware if you take the train, it goes from a different station than the one you but tickets at, and you must pre buy tickets.Train pricey but fun-usually a fashion parade and a folk dance exhibition. If you buy a tourist pass in Cusco, it will save money going to the sites in Cusco, and also gives admission to a folkloric dance show which has a costume museum-worth going to even if you're not big on dance.
If you go south of Lima, Nasca lines are a bit disappointing. Right beside a highway-can see them from a lookout but really need to do the helicopter flight which is pricey.
Can do a tour where you go to Lake Titicaca and can stay overnight with a local family and also go out to one of the floating islands made of reeds that people live on.
It doesn't matter where you go in Peru, there are ruins-some not yet open to public and some still active digs. My tip research the ones near where you think you might travel-you'll enjoy them more if you know a bit about them. Enjoy!