Wendell Cox used this as a reference when he said X'ian at its greatest geographic expanse was about 30 square miles:
http://www.amazon.ca/Chinas-Golden-Age-Everyday-Dynasty/dp/0195176650
That means a density of around 40,000 ppsm.
It wouldn't be difficult to imagine densities of over 100,000 ppsm without even taking into account crowding for the poorer districts.
The densest blocks of Dubrovnik for example probably have about 80% of the space dedicated to buildings, 20% to streets, and no yards. For the walled city overall, maybe around 50% is buildings. Assuming an average building height of 3 stories and 500 sf of space per resident, you get 84,000 ppsm. Most of the ancient cities would have had a fair bit less than 500 sf per resident.
What are you basing the 60-80 square miles of Rome on? Most maps suggest something more around 3-4 square miles.
Even the wealthy parts of these ancient cities were likely fairly dense though. The homes and palaces were large and grand no doubt, but also house far more than a typical modern family. You had large families with many children, and a great deal of servants/slaves. While there were great big rooms and courtyards, the structural densities were still quite high. And for instance, you probably had one large kitchen for the large wealthy family and the army of servants. The children of the wealthy likely still shared bedrooms. You might have had one or two large rooms to accomodate guests, but when you consider how many people lived there (including servants) it wasn't that much.
The amount of space dedicated to open space was typically quite low. Streets were very narrow, yards rare (a few courtyards, mainly for the wealthy), a few market squares, and a few spaces around palaces for parades, colliseums and such.