Seleucia on The Tigris is Babylon of 1 Peter 5:13.

 Seleucus Nicator founded Seleucia in 305 BC, in order to quickly make it a Metropolis he forced most of the population of Babylon to resettle there, there is a tablet dated to 275 BC recording this.  It spent very little time as the actual Capitol of the Seleucid Empire, but it did spend most of the 3rd and 2nd centuries BC as a larger city then Antioch.

Diogenes of Babylon was a Stoic Philosopher commonly referred to as being "of Babylon" but he was actually born in Seleucia and neither city is where he spent most of his life, he was educated in Athens and obviously mostly lived there during his time as head of the Stoic School based in Athens until he died around 150-140 BC.

1 Maccabees 6:4 and 2 Maccabees 8:20 call a City in Mesopotamia Babylon even though it's population is Macedonian.

In 141 BC the Parthian Empire took it from the Seleucids and made it their western capital, but it remained a fully Hellenistic city.

Josephus's references to the city confirm that even the remaining Jewish diaspora of Babylon were in fact mostly living in Seleucia during the first century.  The Jews of Seleucia and other northern Mesopotamian cities revolted during the Kitos War. That of course was a factor in Trajan destroying the City in it's original form in 117 AD.

Hadrian gave Babylonia back to Parthia however and they then quickly rebuilt Seleucia in a Parthian style.  That version of the city was destroyed by Avidius Cassius during another war between Rome and Parthia in 165 AD.  It then became a Sassanian city commonly called Seleucia-Ctesiphon.  This city became the seat of the leading Bishop of the Ancient Church of The East who was formally called the Patriarch of Babylon.

If people really find it so unlikely Peter was in actual Babylon when he wrote his First Epistle simply because some first century sources make it sound like it was a mostly abandoned ruin already, then Seleucia is probably where he was.  It was home to an important Jewish population and Paul calls Peter the Apostle to The Jews in Galatian 2:8.

The idea that Peter said "Babylon" in place of "Rome" to fool Roman officials who might read the letter is stupid.  

1. He doesn't actually say anything bad about where he is, it's only the negative connotations the name of Babylon often has in the Judeo-Christian mind that makes it seem that way.

2. Roman customs officials would have known where the letter was actually mailed from.  So using an easy to interpret as insulting name instead of the real name would have only caused problems.

If Peter meant by Babylon a city other then the exact same city where Hammurabi and Nebuchadnezzar ruled, it would have been the one other similar Greek texts were calling Babylon during the Greco-Roman Era due to being the regional capital and largest city of the region called Babylonia.