We found the greatest concentration of cheap Beijing guesthouses in the area south of Tiamenn Square. the accomodations were with in a two block area with many more around this general area with Beijing cheap hotels and budget accomodations also in the area. We prefered this area as all fo the buses and a couple of metro stations were very close by. If you went close to the Luxury Beijing Raffles hotels you would find another little nest of Beijing cheap accomodations which if you were only going to do the Forbidden City would be good choices.
Best bet 365 Inn, Sakura restaurant both clean guesthouses at really cheap prices for Beijing both offered internet and cheap food on premises. WiFi access would be main reason that I recomend 365 Inn over Sakura but if internet is not real important i really like the layout and atmosphere at Sakura.
Another concentration of Cheap Beijing Guesthouses was just out side the Beijing railway station. Some were setup as guesthouses hostels hotels where all 3 types of rooms would be offered at different price points ussualy the cheapest in the area.
The Central Youth Hostel Near the railway station was one of the nicest hostels they also are a hotel so if you are looking for a hotel near the railway station I can recommend this one to you.
Cheap Charley Asian Travel Tip if you are looking to buy Cheap flights to the rest of China the China Airline Office had the cheapest airfares in China, I had checked the prices for really cheap flights in China on the internet and these were cheaper by almost 40% !