Day 1
Imperial axis: Tiananmen → Forbidden City → Jingshan → hutongs
Book the Forbidden City days ahead (passport required — it sells out). Enter at Meridian Gate by 8:30, walk the central axis for ~3 hours, exit north and climb Jingshan Park (¥2) for the rooftop panorama every postcard uses. Late afternoon: wander the Nanluoguxiang side hutongs and eat dinner at a courtyard restaurant. Roaming photographers near the palace gates will shoot you like an emperor for about ¥20 — ask for a trial shot (试拍) first.
Day 2
Great Wall at Mutianyu — the whole day, no rush
Skip Badaling. Take a direct tourist bus or share a car to Mutianyu (~90 min): cable car up, walk the towers for two or three hours, then ride the toboggan down — yes, a real toboggan off the Great Wall. Weekday mornings you'll have whole stretches to yourself. Pack water and snacks; food at the base is tourist-priced. Back in the city by evening for Peking duck — a half duck at a specialist house feeds two.
Day 3
Temple of Heaven at dawn → 798 Art District or Summer Palace
Come at 6–7am when the park belongs to Beijing's retirees — tai chi, sword dancing, choirs. The blue-domed Hall of Prayer opens at 8. Afternoon, pick one: 798 Art District (free galleries, industrial-chic cafés) if you want contemporary China, or the Summer Palace (boat on Kunming Lake) if you want one more imperial masterpiece. Finish with hotpot.