Daytime Lima is ideal for a cultural trip. Take your Peruvian lady to the Museo de la Nacion (the National museum) to see a summary of Peru's history and then take a cab downtown to see the Cathedral at Plaza Mayor and the changing of the guard at 1:00 in the Government Palace (just across Main Square). After that, you can have lunch and then visit the catacombs at Santo Domingo Church or the Museo de la Inquisicion and del Congreso (Museum of the Inquisition and the Congress). To close out your cultural day, you can visit Museo de Arte de Lima (Art museum) with a Peru woman.
OK some Peru women you will date may be more interested in the fun option. Here are some ideas. Take a bus or taxi and go enjoy the Pacific Ocean. Peru has beautiful sand and pebble beaches less than an hour away; some are great for surfing. Lima also has many beaches, but Peru's best beaches are located outside of town. A walk along the beach with a Peru woman will provide the perfect setting for romance.
If you arrived in winter or are not in the mood to go to the beach, but would like to enjoy some delicious Peruvian seafood ask for cebiche to start. It is fish and/or seafood in small pieces, marinated in lemon juice and seasoned with onion, garlic, chili and other spices. Try some Peruvian desserts also: champus, picarones, mazamorra morada, and arroz con leche.
If you want to relax, go for a walk in Miraflores with your special Peruvian woman and watch artists display their paintings in Kennedy Park. Also visit Larcomar for a nice view of the sunset. If you and your Peruvian lady are feeling romantic, go to the Puente de los Suspiros (Bridge of Sighs) in Barranco. There you can also see the old spirit of bohemian Lima, enjoy a drink, and find out if there is going to be a good concert later.
In Miraflores, you can do paragliding. Two hours away from Lima to the south you can do some canoeing, rafting and horse riding, too. If you want something much more relaxing you can go to the zoo. The zoo? Women in Peru love to go and there are hundreds of animals you won't be able to see anywhere else.