Some Romans certainly felt a nationalistic identity of sorts, or at least pretended as they did. One good example is the writer Aelius Aristides, who delivered a famous panegyric to Rome and the emperor Antoninus Pius. Here are a few choice quotes:

… it is not easy to decide which is the greater: the superiority of this city relative to cities that presently exist, or the superiority of this empire relative to all empires that ever existed…

You have divided into two parts all men throughout your empire... everywhere giving citizenship to all those who are more accomplished, noble, and powerful, even as they retain their native-born identities, while the rest you have made subjects and the governed. Neither the sea nor the great expanse of intervening land keeps one from being a citizen, and there is no distinction between Europe and Asia.... No one is a foreigner who deserves to hold an office or is worthy of trust. Rather, there is here a common "world democracy" under the rule of one man, the best ruler and director ...

Let us pray that all the gods and their children grant that this empire and this city flourish forever and never cease until stones float on water and trees cease to put forth shoots in spring, and that the emperor and his sons be preserved and obtain blessings for all.

The ideas of Aelius Aristides are particularly interesting, because he was a Greek. By this time many local elites around the Empire were strongly identifying with Rome and the concept of the Res Publica (meaning ‘public affair’ and not ‘republic’ in our sense). Many local elites possessed Roman citizenship as well as a local citizenship, and apparently accepted this duality quite happily.