Walk through Tiananmen Square and tour the Forbidden City (Palace Museum) to see imperial halls and learn Ming-Qing history; Forbidden City generally opens 8:30–17:00 (check seasonal times).
Climb Jingshan for panoramic views over the Forbidden City and stroll nearby Beihai Park for a calm palace-lake contrast; Jingshan opens early into evening.
Head to Mutianyu section (less crowded than Badaling) early; cable car and toboggan options available — Mutianyu general opening ~8:00–17:00 (seasonal).
Visit Temple of Heaven (park and imperial altars) and then take a short Hutong tour by rickshaw to experience traditional courtyard life; Temple of Heaven park open early until evening.
Head to Shanghai Tower (observation deck) or Oriental Pearl for a bird's-eye view over Pudong and the Bund; observation decks open into the evening (check hours).