One day is really a short time, but I will try to recommend the most indispensable and attractive places or activities in Lima.
To begin, a good option is to take a short tour that allows you to know in a single tour the main areas and traditional neighborhoods, I recommend one that leaves from the LarcoMar Shopping Center in Miraflores in the morning (9:15 am), lasts only 4 Hours and is quite complete since you visit the modern part and the colonial part of Lima, starting with the traditional district of Barranco (famous for its Bridge of Sighs and for being a bohemian neighborhood), followed by the district of Miraflores crossing its Central Park or Parque Keneddy (lately called "Cats Park" due to the large number of cats that inhabit it), you can have a panoramic view of the Archaeological Complex of Huaca Pucllana and then continue to the Historic Center of Lima where You will be able to appreciate its most representative buildings such as the Palace of Justice, San Martín Square, Plaza Mayor, Government Palace, Lima Cathedral, Archbishop's Palace, Municipal Palace, Desamparados Station, San Francisco Convent , One of the most emblematic churches of Lima that is characterized by its unmistakable and striking yellow color of its façade, here you can enter below it and tour its catacombs. In the tour you will also find beautiful houses, colonial balconies and some other churches
If you get up early you can take advantage of a rich breakfast before the tour and enjoy a nice view of the sea. Restaurant Mangos or Tanta are very good options,
At the end of the morning tour is time to enjoy the Peruvian gastronomy; Restaurants there are many and very good, there are several lists on the internet of top restaurants in Lima so before recommending one in particular I will tell you what dishes / drinks you can not fail to taste: First there is the ceviche (made of fish or mix seafood, if you are not very tolerant to the spicy I advise you to advise the waiter to prepare it with no hot sauce), anticuchos (my favorite entry!, are a kind of kebabs of heart of beef, they are usually served with Potato and corn or corn), papa a la huancaína (they are slices of potato sancochada with a delicious cream based on milk, chili, cheese, crackers or bread and some spices), lomo saltado (beef tenderloin sautéed with onion wedges and Tomatoes, spices and accompanied with French fries and rice, sounds simple but when you try it, it really is a delight), ají de gallina (chicken or frayed chicken mixed with a cream based on broth, milk, chili, pecans and a base dressing, which is accompanied with potatoes sancochadas, rice and olives), then there are also grilled chicken (pollo a la brasa), rice with duck, stuffed rocoto, carapulcra and I better stop here because I am already opening the appetite ...
Among the typical drinks you can find pisco sour, chilcano (both based on pisco) and a very rich refreshment based on Peruvian purple corn, chicha morada.
In the afternoon you could visit some Museum, the most complete and visited are: Larco Museum, Gold Museum, Lima Museum of Art MALI, Museum of Archeology and Anthropology. Another good option is the Citadel of Pachacamac, ruins located at 30 min. Of Lima (in a little more than 3 hours you can visit them and be back in Lima).Take time to shop !! In Miraflores at Av. Pettit Thouars (very close to the Ovalo of Miraflores) are the Craft Markets along 2 to 3 blocks, in case you want to buy some alpaca garment, silverware, paintings or just bring some souvenir to your family /friends. There are many curious things and of all price, they start to close the posts from 8:00 pm.
At night you could visit the Reserve Park and tour the Magic Water Circuit that has the Guines Record as the largest Fountain Complex in the world in a Public Park; In addition to touring its 13 ornamental fountains you can enjoy its main show that is impressive as the joyful movements of the waters are mixed with games of multicolored lights and images that dance together to the rhythm of music. The Park opens from Wednesday to Sunday from 4:00 pm and the first Show is at 6:30 pm (ideally visit at night).
Another good option for the night is to visit a Restaurant with Dinner Show, the best known and recommended in Lima are Brisas del Titicaca (in the Center of Lima) or La Damajuana (in Barranco to 5 min of Miraflores), in addition to the dishes Typical Peruvians offer a typical Peruvian Dance Show, a real show.
And if you still have energy you can go to a bar or lounge, in Miraflores and / or Barranco the majority are concentrated, they are very good and for all tastes, I leave you with some options: Sukha Buda Lounge, Avalon, 5th. Avenue, Bizarro, Gothica, Victoria's Bar, La Trastienda, Green Crocodile, Picas Bar (the latter have live music), among others.
Here you can find more tourist places of Lima and options of tours with discounts throughout the year.
You just need a lot of desire and a good camera to enjoy this day to full;)