Where can you go in a zero gravity chamber?

There is no such thing as a zero gravity chamber. The only way to experience weightlessness is in freefall. There are planes that you can board which will go into dives up to 30 seconds long. During these dives the planes are in freefall. Since you are falling at the same rate as the plane is, you will seem to float around the cabin and will feel weightless. It is the same reason that astronauts in orbit are weightless.