Planning a 7 day trip. Interested in seeing the great wall and the taking the bullet train?

I think 7 days can cover Shanghai, Beijing and Xian, but the travel may be a little bit rushed. I suggest the following for you, you should adjust it according to your flight time. Hope it helps you.
Day1, Night cruise on Shanghai Huangpu River, the Bund
Day2, Yuyuan Garden, afternoon bullet train to Beijing.
Day3, Tiananmen Square, Forbidden City, Temple of Heaven
Day4, Badaling or Mutianyu Great Wall, Hutongs.
Day5, Summer Palace, afternoon bullet train to Xian
Day6, Terracotta Warrior Museum, City Wall, Big Wild Goose Pagoda
Day7, fly back to Shanghai.