Want to feel the real Beijing? Only visiting the sightseeing is not enough. You can also go to the local family who live in the court-yard in Hutong for many generation, you may know the local culture and history by the most informative way. More over, some family provided home stay (a bed and a breakfast), you may live with them and feel the the Chinese way of living have a cup of tea and chat with the host at afternoon, you may know better about the history and the culture of China. Not only will you learn some Chinese, but also how to make dumplings.
This is a cheaper and easier way than stay at other palace. So next time you visit Beijing give a try to staying in a local home.