EDIT: Just noticed this is an OLD thread, from AUGUST.
It would be helpful if you gave a little more detail, like why you are in Panama City, and for how many days. Is it in connection with a cruise? The main reason I ask is that not all areas of Panama City are considered safe for naive tourists alone. OTOH, Colon, at the other end of the canal, there is almost NO place safe for an unaccompanied tourist. We were bussed by our cruise company from the Panama City arrival days to Colon, for embarcation. It's quite a long distance. The hotel warned (yes, I know they have an economic interest ... ) to use only their approved car service company for our independent explorations in Panama City.
If you are asking, "Is the canal a security zone that I am not free to stroll the length of at leisure?", that is correct.