For one journey that unlocks Chinese history, take this ancient-capital route: Beijing (Yuan/Ming/Qing), Xi'an (Qin/Han/Tang) and Luoyang (Han/Wei), linked by high-speed rail, about 8 days in total.
Days 1-3, Beijing: give the Forbidden City at least half a day, climb Jingshan Hill for the full-palace panorama, hike the Great Wall at Badaling or the quieter Mutianyu, and stroll the Shichahai lakes at night.
Days 4-5, Xi'an: about 4.5 hours by train. See the Terracotta Army — the "eighth wonder of the world" — cycle the ancient city wall, try yangrou paomo (lamb stew with bread) in the Muslim Quarter, and watch the Giant Wild Goose Pagoda light show.
Days 6-7, Luoyang: about 1.5 hours by train. The Vairocana Buddha at the Longmen Grottoes is unforgettable; the White Horse Temple is China's first Buddhist temple; and Luoyang water feast is a local specialty.
Day 8, return: the Longmen high-speed station connects directly to Beijing or Zhengzhou airport. Winter is cheaper and quieter; summer is hot — prepare accordingly.