In Beijing, I advise you to visit the essence of Beijing which include Great Wall, Forbidden City, Summer Palace, Lama Temple, Temple of Heaven, Ming Tombs, Tianmen Square. As for another city, I suggest Xian. You can consider the following itinerary.
Day 1, Arriving in Beijing. If you arrive in the morning, have a good rest and explore the Hutong area in the afternoon.
Day 2, Stroll around the Tianmen Square which is surrounded by many significant buildings including the Museums, Chairman Mao's Mausoleum and Heavely Gate. Then visit Forbidden City which faces Tiananmen Square at very close distance. In the rest of time, you can visit other attractions.
Day 3. Drive to climb the Great Wall in the morning. Then drive to visit Ming Tombs.
Day 4, In the morning, pay a visit to Temple of Heaven. In the afternoon, take flights or night train to Xian.
It is possible to visit Xian in two days.
If you take flight, it takes you about nearly two hours. After arriving in Xian, take shuttle bus to the downtown area and stroll along Xian Muslim Quarter Area after a short rest. Day 5, visit Terracotta Army. You can take coach bus at the east of Xian Railway Station. It takes you about 40 minutes and about 2 hours to visit Terracotta Army. In the afternoon, you can visit Shangxi Historical Museum (free) and Big Wild Goose Pagoda, these two are about 10-minute walk
If you take night train, you can arrive in Xian in the morning of te fifth day. And take the coach bus at the east of Railway Station to visit Terracotta Army. In the afternoon, visit Shangxi Historical Museum (free) and Big Wild Goose Pagoda.
But you have to book hotels and transportation beforehand if you plan an independent travel.