Bundi, you'd be well served to do a search and you should find more than enough information. To get you started though, I'll list places you can go/see in Beijing (in no particular order).

Great Wall (do the hike from Jingshanling to Simitai, driving there and back along with the hike will take a whole day and its the best way of seeing the wall), Tiananmen Sq, Forbidden City, Summer Palace, Temple of Heaven, Hutongs (near and around Liqun Duck Restaurant are amongst my favorites), Yonghegong Lama Temple, The Houhai/Qianhai lakes (hutongs that are gentrified, have some kitchsy shops along with tacky ones, ditto for bars and restaurants, though on a normal day if you walk around you'll see plenty of ordinary people playing chinese chess/cards), Beihai park, 798 Art District, Ming Tombs (never been myself), Military Museum...

That should be a start.