Categorical Data - Hallway traffic flow comparison

I have collected data on the number of people that move through different hallways around my campus and counted them as belonging to one of three possible categories. Each person was recorded once as having either walked through, looked or stopped in the hallway, and I've collected data in 4 different hallways. I also collected the same data at a second point in time to see if there was a difference between time one and two.

I want to compare the rate of looking, stopping and walking across the three different spaces, and within the one space, if there is a significant difference between looking and stopping between time one and two.

I'm pretty sure that my data are discrete (definitely not continuous!) because it's count data. Is chi-square appropriate? I'm just not sure what test to use.