One of the history buffs wil have to answer this, but it's my impression that there wasn't a real "capital" in the Seleukid kingdom like it's portrayed in RTW. The administration was decentralised, through satrapies. Of course the king was the central authority, but I'm not sure wether there was a permanent court at a physical location.

It was a long time ago, but I think in my Seleukid game I switched the capital to Seleukeia. That was more a monetary decision than anything else though, there are more provinces there so it saves money in garrison costs and tax levels. I changed it back to Antioch when I got my finances in order and started conquering Asia Minor.

I don't know how Babylon was administered by the Seleukids. Generally, I only install III or IV governments if it gets you access to specific units* and IIRC that's not the case for Babylon.

* two exceptions:
- when a newly conquered region is particulary rebellious I often make it a IV with a client ruler at first so that it's more easily subdued
- when an enemy city already has the largest market and most other buildings, and the region doesn't offer any good factional units anyway. Good example: the Koinon Hellenon cities for the eastern Greek factions.