To minimize jet lag, stay active until at least 9 p.m. First, have a swim and a light lunch while taking in the Hilton's social scene. In spring and summer, Arab families rent the spacious cabanas surrounding the grassy pool area and camp out en masse. Then ask the concierge to arrange a small picnic for later (a bottle of wine, a few snacks), a car and driver ($25–$35 per hour), and a reservation for dinner at an outdoor table (weather permitting) at the Citadel View Studio Misr restaurant, in Islamic Cairo's Al-Azhar Park (20-2-510-9150; entrées, $18). An hour before sunset, picnic in hand, head with your driver a few hundred yards south down the Corniche al-Nil, the riverfront thoroughfare, toward a felucca at Dok-Dok landing, located between the Grand Hyatt and the Four Seasons. A boatman will sail you along the Nile as the sun sets and the bridges fill with couples enjoying the soft evening air (feluccas, about $7 per hour). After darkness falls, ask your driver to take you to the 74-acre Al-Azhar Park, created in 2004 by the Aga Khan Trust for Culture on what was a 500-year-old rubbish heap. No alcohol is served at the Citadel View Studio Misr restaurant (the driver will wait), but the mixed grills are delicious and the view magical: You'll see the illuminated Citadel, the fortress built by Saladin in 1176 to defend the city from the Crusaders, and its iconic Mohammed Ali Mosque (1830–1848).

Before you succumb utterly to jet leg, there is still the drive back through the bustling streets—pedestrians dodging traffic, men in cafés sucking on water pipes, here called sheeshas (pictured bottom right)—all the intoxicating hubbub of a city that lives on desert time, where nighttime is the best time. Keep your eyes open: Cairo is the unofficial capital of the Arab world, and this will give you a feel for the texture of everyday life.

Day 2: Giza, Memphis, and Sakkara
It will be painful, but get up at 6:30 a.m. (you'll be glad you did), and after a big buffet breakfast—standard in all of Egypt's hotels—meet your guide in the lobby at 7:30 for the drive to the Giza plateau and its three great pyramids and Sphinx, about ten miles southwest of Cairo. The pyramids "open" at 8 a.m., and you want to be there when they do. Although chronologically speaking you should begin with the site of ancient Memphis and its necropolis of Sakkara (the first capital of a united Egypt, established in 3100 b.c.), the pyramids of Giza, dating from about 2500 b.c., are the country's ur-monuments, and the Great Pyramid (a.k.a. Khufu's) is the only remaining Wonder of the Ancient World, so you might as well start with a bang. Your guide will give you tickets for entering whichever of the three pyramids is open that day, and then you'll be ascending and descending narrow, low-ceilinged corridors, finally leading into the King's Chamber, where the sarcophagus once stood. Note: This is not for claustrophobes, and it's hell on the hamstrings. When you emerge, 45 minutes later, circumambulate the base of the pyramid, looking up as you go: There's no better way to fully comprehend the structure's enormity, nor the lust for immortality that inspired it. You will now be ready for some air-conditioning, so stop at the small Solar Barque Museum, on the south side of Khufu's pyramid. It houses the 140-foot cedarwood barque belonging to the pharaoh, which was discovered buried in a pit adjacent to his pyramid. Walk to the Sphinx, ten minutes downhill. Although riddles remain, the human head on the feline body probably portrays the pharaoh Khafre, as the beast was carved from the bedrock leading to his pyramid. Then it's time to stop for lunch at the Mena House Oberoi's Khan El Khalili restaurant, which sits in the shadow of the pyramids (20-2-590-3788; entrées, $15–$22).