Beijing is a centralized city consisting of urban and rural areas. Thus, the official map of Greater Beijing in Russian consists of 14 urban districts and 2 counties.
Hotels on the map of Beijing are concentrated in the Old City - it is located on the territory of Xicheng and Dongcheng districts. These districts were once surrounded by a high fortress wall, which is now replaced by the 2nd Ring Road.
The Tiananmen Gate is unofficially considered the border of the central part of the city - it once served as the entrance to the city. So tourists can confine themselves to a map of central Beijing, where all the sights are concentrated.
The answer to the question of which neighborhood in Beijing to stay in is quite simple - within the Second Ring Road. Among the neighborhoods in downtown Beijing:
Dongcheng - once home to China's rich and bureaucrats, this is where the main sights in Beijing (Forbidden City, Confucius Temple, National Museum of Beijing, and others) are located today.
Sicheng is the west of the Old City, home to the Xidan shopping district, the city zoo and the beautiful Beihai Park.
Chaoyang is one of those neighborhoods where affluent tourists are better off. It has the most expensive bars and restaurants (Sanlitun Quarter), the embassy quarters and Beijing's business center.
Haidian is a university district, and is home to Peking University (located in the former Imperial Gardens) and other universities. In Haidian, Yabaolu Street is home to Russiatown, one of Beijing's main wholesale clothing centers. By the way, Beijing's Yabaolu neighborhood is considered dangerous, with aggressive bicycle rickshaws and local gopniks often trying to "divorce" Russian tourists.