Hi, since your time in Beijing is rather pressed, I suggest u visit Badaling among the many Great Wall sections for its popularity and easy transportation. You can take bus no.5 at Tiananmen Square East and get off at Desheng Gate Station. Take bus no.919 at Desheng Gate Station and arrive at Badaling Great Wall.

Of course, you can visit all the sites by yourself. Forbidden City is a good start from where you can go to other sites very easily, such as Tiananmen Square which is in front of it and from Tiananmen, you can go to Badaling as I told you in the first para. and Wangfujing Street where shopping is a must.

To stay near the Forbidden City is a nice choice. The Park Plaza Wangfujing is good. It is a four star hotel with good location.

In Xian, you are suggested to see the Terracotta Warriors, Big Wild Goose Pagoda, city wall and take yummy snacks in the Muslim Street around the Drum Tower. Good trip!