Yes the Forbidden city is walkable from this hotel. You can visit on your own. You can rent an audio guide or hire a guide at the entrance. Bring your passport to buy a ticket. Note that it closes on Mondays.
For the Great Wall there are many sections. Badaling is one hour away and reachable by bus. As a result of being easy to reach, it is the most crowded section. Mutianyu is 1.5 hours away by car. You can hire a driver for the day. Cost is about 600-800RMB. He can drop you at another site afterwards such as the Lama Temple or Summer Palace (depending on time of day). You can find a driver here (much cheaper than at the hotel) Newest Classifieds posted today | the Beijinger In the past I have used Mark: Mark's Mutianyu great wall Tour ,Beijing tour guide, English speaking driver, Beijing private tour,