Arrive at Beijing Capital International Airport. Take Airport Express Line to Dongzhimen (CNY25), then Bus 619 to Houhai area. Walk to Yi Se Hotel (within 1km of Indian restaurant Ganges). Cheapest option costs ~CNY30 and duration about 1h45m.
Take Bus 916 Express from Dongzhimen Bus Station to Huairou North Station (1h30m). Then take local bus H23 or taxi to Mutianyu entrance. Entrance fee CNY45. Toboggan ride approx CNY80. Open 7:30am-6pm.
Take Bus 303 from Bei Hai Park to Summer Palace (approx 50 mins). Entrance fee CNY60, open 6:30am-7pm. Rent bicycle for CNY40/hour to explore larger grounds.