The Quarry is the place that the group stays for most of Season 1. It is right outside of Atlanta. The group thinks it safe until one night a herd of walkers comes through and wipes out about half of the group. The next day, the group leaves for the CDC.
Center for Disease Control:
The group travels to the CDC after the quarry is attacked. There they find only one scientist left, and they only stay for one episode because the power generators run out of fuel.
At the beginning of season 2, the groups RV breaks down while on a highway and they make camp there until they find Hershel’s Farm.
They discover Hershel’s Farm after Rick’s son, Carl, is shot because of a "hunting accident." The group seeks medical help there for not only the shot, but also for a bad cut on T-Dog’s arm. At the end of season 2, Carl fires a shot while a herd is wandering by and the herd is re-directed toward the farm. It is over-run and the group is forced to leave.
The Prison is found when the group is on the road. Daryl and Rick go hunting and find it. They stay in the prison for about a season and a half until the governor comes in with a tank and destroys it.
After many weeks of wandering, the group finds themselves at Terminus. But it is not what it seems so it gets destroyed and overrun.
Not much is known about the hospital, some of the group is there currently.