Thank your lucky stars that the geography of Beijing is pretty easy to get to grips with. Currently, to most foreigners only the area within the 4th ring road is interesting, with all beyond rather Chinese 老百姓 or migrant worker territory (except perhaps 望京 in the northeast). However, there has been a push-out movement in recent years with foreigners slowly (and reluctantly) moving closer to the periphery as rental rates are rising. Generally speaking, the closer you are to the center (i.e. the Forbidden City) the more comfortable your life will be; comfort, however, will cost money.
From left to right
If you start out at the Forbidden City, you basically have 长安街 running east to west. The shiny boulevard roughly separates north from south Beijing and is something of the main traffic artery of the city. Along the street you will find Beijing West train station, the Military Museum, Financial Street, Xidan, the Opera House, the Forbidden City, Wangfujing, Beijing central station, 国贸 Beijing World Trade Center etc. A bike ride along the road, especially late at night is highly recommended.
Thank you Google maps: the red line is 长安街
The ring roads
Beijing then features six ring roads circling the city in more or less even distances. The first ring road does not officially exist but are the streets leading around the Forbidden City. The 2nd ring road leads around the “first ring road” in about 2-3km distance. From here the distances from ring road to ring road increase along with the total lengths of the ring roads. Within the 2nd ring road you will find most of what used to be the ancient city of Beijing, e.g the hutongs. If you come across hutong like architecture outside the 2nd ring road it is probably not authentic. Between the 2nd and 3rd ring roads you will find the newer areas and much of the business heart of Beijing. Professional services firms, trade firms etc. will oftentimes have their offices in this area. Between the 3rd and 4th ring road you will find any larger modern infrastructure plays that simply could not be accommodated closer to the center. You will find many residential apartment blocks there housing more people in one compound than in many smaller US or European cities.
The ring roads facilitate everyone's lives
The rich north and poor south
Interestingly, there is a tendency for the northern part of Beijing (i.e. north of 长安街) to be more shiny, modern and important. All the best universities, hospitals and other important bits of infrastructure are situated in the north. Perhaps building the new airport in the south is supposed to address the problem but, be it through coincidence or planning, the truth is that the south seems like a unloved foster child when facing off with its proud northern brethren.