A few things
1) Regarding Hungary - I'm not convinced, that it serves the Romans well to leave Hungary alone long-term. They want them either as an ally, or part of them, and depending on the PoD, that could be relatively easy (it wouldn't be the first time that a future King of Hungary was named Heir to the Roman Empire). The Ottomans did that with the Girays of Crimea, we could see the Romans sign a treaty with Hungary that binds Hungary to the Orthodox Church (yay for Orthodoxy) but in exchange they become the Second Family of the Empire, effectively the heir-apparent. So I think a Romano-Hungarian union is a strong possibility.
The reason for all that? Just as Anatolia is important for the Taurus, Hungary is important for the Carpathians. They make a stronger border than the Danube, and create incredible defence in depth for the rest of the Empire.
2) Middle East / Southern Strategy
Anatolia needs to be secured, fullstop. End of Story.But you've got that.
Syria - Going south is dangerous, depending on how you do it. If you stick to the coast, behind the mountains? That'd be sensible, mostly. But it still leaves a very long border for a very thin strip of land behind the Syrian Coastal Mountain range (also known as the Bargylus). It is however the best land in the area. You could go down here, but I can only imagine that it'd be costly to defend unless you can secure inland cities. Perfect example is Damascus - it effectively is a lynchpin for a Levantine strategy, as its strong and wealthy enough to provide a base for invading the Levant. I wouldn't recommend this route, not until its either very easy, or the Romans are doing incredibly well.
Egypt - unless you have a politically secure Syria/Levant, Egypt is a massive gamble, for at best an at-risk navally-reached province, or more likely, effectively a puppet state/vassal. It is a hell of a risk, but the reward could be massive if the internal politics can be stable.
If you wanted to get Syria and Egypt, as this Empire, if I was your Roman Emperors, I'd be entirely supportive of Crusade after Crusade going after Egypt and Syria. Completely break it down, there is a chance the Crusaders get their acts together and unite, which is a different problem, but once Anatolia is secure, a divided Levant, Damascus, Egypt are great targets.
3) Highlands Strategy
Caucasus - This is messy, but good. It also ties into Anatolia via the Armenian Highlands, which I would assume you'd want to secure anyway to solidify the eastern border. The region is easily accessed by sea post-conquest via the Black Sea, and is great for a NE border territory, and easily defended from that direction. Your problem is your exposure to the Iranian Plateau, and Mesopotamia. Rather than just the Taurus, you also have the Zagros and Anti-Taurus to worry about. However this does give you the advantage that if you did go into Syria, you have the ability to come from three directions, or at the very least two and have an army that can bring the front quickly into Mesopotamia, rather than Syria. In fact this was done in an Age of Miracles as a strategy to address a strong Ottoman Persian Empire.
4) Western Strategy (I think this is the most relevant)
South Italy - as mentioned, the Normas are a pain, getting the region secure is a good flank, and allows the Romans to position a Navy to take control of Mediterranean trade. Not the most important unless the Romans are opening more trade between the Middle East and Europe. What it does do however is provide access to the most important targets, Africa, and the Straits.
North Africa - I would expect the Romans would want to be able to control access into the Mediterranean, much as they control access to the Black Sea. This means a strong base in Gibraltar, Ceuta, or Tangiers (using a mole if needed). Securing South Italy gives them strong control over the Med itself, but not control over the Western Med. Taking North Africa, rather than Egypt, is still a naval jump, but is also less vulnerable to the rest of the Middle East. Plus, assuming it isn't butterflied away, this is a hotbed for piracy in the Western Med, and so the Romans could negotiate some assistance under the guise of ending Piracy, which ties nicely to securing Roman logistics. They need to learn how to fight in the region again, especially some sort of Desert Cavalry to secure the frontier, but taking the coast opens the Atlantic to the Roman world, and if it can be secured, locks the Romans as a prime power to rival Spain, Britain, and France during this time (in terms of interests, at this point the Romans would be likely stronger than any of these individually, or too fragile to persist at this level, situation permitting).
At which point the Romans can really start looking at the rest of the world. Get in on Colonisation. Address the Papacy. Respond to the Reformation in a way to serve Roman interests. Etc. It could be as simple as the Romans and English allying to ruin Spanish interests. The Romans might get interested in securing West Africa. There are still loads of other problems - notably, securing the Sahara, and the Western Strategy still hasn't addressed the European, Middle-Eastern or Highlands concerns at all.
The only thing I think you need to address is well, Russia. I don't mean all of Russia either, I specifically mean the Ukraine, Crimea, and Circassia. Those are frontiers for the Romans, and the Russians, the two major Orthodox powers. If you have Cossacks rise, do they pick sides? Do the Romans effectively rule (on paper) a large Cossack Nation on their northern border? How relevant are they? Does the Ukraine replace Egypt as the Breadbasket of the Empire? Or are the Cossacks able to use the Romans and Russians against each other to create an early Ukrainian Hetmanate (or equivalent)?
