The primary thing to keep in mind is that when you travel around and see ancient sites, most of what you see is Roman, which I am defining in a strictly chronological sense). The Library at Ephesus, the theater at Aspendos, the temple of Baalbek, all of these were constructed during the period when Rome had imperial power over the whole of the Mediterranean. The Roman empire set off a "building boom" across the region--a fun illustration of this is in the city of Athens, where you can compare the classical Theater of Dionysus with the Theater of Herodes Atticus, which is several times bigger, or the Parthenon itself with the Temple of Olympian Zeus. There is a lot of debate about what caused this--two useful poles can be conceived of with a historian like Peter Temin, who believes this was caused by economic growth driven by the security brought by Roman unification of the Mediterranean, on one end, and one like Peter Bang, who believes this is really just a matter of guns and butter dividend rather than real economic growth.

Beyond that I do not really think there is much to accomplish by coming up with something like a checklist of features that a Roman or Greek city might have. There certainly was regional variation (Amphitheaters were uncommon in the Greek East, North Africa had a profusion of "Capitoleum" style temples, the eastern provinces tended to give religious structures centrality in their urban design, etc) but in general, the difference between, say, Athens in 150 CE and Athens in 400 BCE was much greater than the difference between Athens in 150 CE and Naples in 150 CE.

That said, if you want a thumbnail sketch about cities in classical Greece and under the Roman empire, I think Peter Connolly's The Ancient City provides a good place to start. It is somewhat out of date and is a tad too schematic, but it is beautifully illustrated (seriously, I can just pore over Connolly's pictures) and is a sturdy base before delving into the tougher meat of the archaeology.