Looking over some real life city population density stats i have come up with a approximation that may help you out.
Boston is a busy but not too crowded city. It has a population of 589,141 a land area of 48.43 square miles and a population density of 12,165.8 per square mile. But if you think about the taller buildings which allows for more people to live on top of each other it is easy to see that the city would feel much more crowded if it was limited to single family dwellings. (I lived there in my youth and three story houses divided up into apartments is common as well as apartment buildings of four or more floors with multiple units on each floor.)
So i would suggest for the sake of argument we cut it down to 5,000 people per square mile which would give you something in the range of five or six square miles for your city if you want it to seem to be teeming with people. (People ready to slit each other's throat just for some breathing room.)
I live in Las Vegas and we have a bit more room here, but there are certainly people everywhere you go. We have about 2000 people per square mile, but keep in mind there is plenty of undeveloped land here in the city. You can drive down a street inside the city and be looking at desert.
When you see these people they are usually in their cars going someplace else. I imagine if they were walking on the street it would look like a festival was in progress.
All this is a round about way of saying i think your city would do well at about 5 by 3 miles and be busy without driving people into the wild surroundings. Six by four would also seem good. The other alternative of course is to keep your original size and increase the number of inhabitants. (Besides, what would people do in their spare time stuck inside an isolated city with danger outside the walls but get to know each other?)