What to do - arriving early morning Rome

Just take your time go to a cafe or McDonalds (if you find a cafe too intimidating). The plane arrives at 6:30 am, but it can take 30 minutes to 2 hours or more to go through passport control, retrieve your bags if you are checking any, getting transportation to your lodging, and then getting from the airport to the area where you are lodging.

Are there any cafes at the airport?

Most airports have that info available on their websites

http://www.adr.it/en/web/aeroporti-di-roma-en-/eat-drink-guide-1

Is it Leonardo De Vinci International Airport you are arriving at?

Google it if it is and you’ll see how ultra modern it is and what cafes might meet be to your liking.

Between landing, getting bags, getting through immigration and customs, having a coffee at the airport, taking the train or cab into Rome, and getting to your hotel, you won't have long to wait before 10:30.

Try the Time Cafe at Rome's airport. Time Cafe is in the departure area of Terminal 3.

https://www.tripadvisor.com/UpdateListing-g656615-d10390960-Time_Cafe-Fiumicino_Province_of_Rome_Lazio.html

There is also a Chef Express and Vacanze Romane where you can have a snack in the arrivals area of Terminal 3.

There are multiple cafes at Terminal 3 arrivals level and another at the airport train station. I'm guessing you'll have about 2 hours from clearing immigration and collecting your bags until you need to head into Rome, so you might even consider the short walk to Terminal 1 where I think the arrivals level cafes are better and less busy. From there you could either walk back to Terminal 3 for train or bus into Rome, or just catch a taxi directly to your accomodation at Terminal 1.

Your other option would be to head straight to the area of your accomodation and find a nearby cafe where you can have a cappuccino and pastry and read or surf the internet until you can drop off your bags. I would check Google Maps to make sure there is a nearby cafe before doing so.

Where are you staying and what was your plan to get there?

If you would be going through Termini, you could stash the bags in a locker or left luggage place and take a walk and hit a cafe. Even a cafe at Termini would be better people watching than the airport.

Even then, there are better options than the airport, if plan was to take a cab to your lodging, go ahead and do that, or at least get close. Google to find a nearby cafe and just be dropped off there.

The last thing I would do is spend 1 extra minute at FCO after my plane has landed.

See if there is a luggage storage facility near your hotel. On a recent trip, my wife and I had about 4 hours to kill in Paris. We dropped our bags off at a Nannybag location. The price was not bad (only a few Euros per bag). This gave us the freedom to do whatever we wanted to do. I just checked and Rome has many Nannybag locations.

Hi...
Not related to your "what to do question" but on arrival at customs there are the "European Passport Holders" Lines and "the rest of the world Passport" Lines. With your Australian passport, ask if you can join the Euro line, our Aus passports can be read by the "Euro" scanners.
We were in Milan in late July and an attendant noticed our passports and escorted us back thru the very long line into the almost empty Euro line. We arrived at about 6:00am from Singapore, and the Euro Line cleared even before "the rest of the world" line even started processing.

"What to do question",
With only one bag each, don't stay at the airport, get into the neighbourhood you are staying in, and sit it out with a local breakfast a morning coffee.
Google street view before you go to get your bearings.

regards

Thank you so much for all your suggestions. I will aim for the European Passport line, grab our bags and head to Trastevere, where our airbnb is, and grab a coffee and breakfast. So looking forward to it!

Are you planning to take the train into Rome? If so, we typically take the local/regional train (located in the same location as the express train) to the Trastevere station. We then pick up a tram to take us deeper into Trastevere. We have found the local train/tram combination to be more direct and very easy. There are 2 trams (3 and 4). I always see which one is closest to my lodging. Trastevere has many wonderful cafes for early morning coffee and snacks.

Hi Becky, we are planning to get a taxi because there are 3 of us so almost worth it. Plus a long flight so I don't know if I'll have the brain power to negotiate train and tram! Need coffee first! Any cafe recommendations?

I would google the neighborhood of my hotel or apartment and go to a cafe nearby. I have done this. You won’t have too much extra time anyway. I agree with rd. The last thing I want to do is sit in an airport of a city to which I am arriving.

Makes sense to take a cab with several people. As far as cafes go, agree with Wray, Google cafes near your lodging to see what’s recommended. Then you could have your cab just drop you off there.

After you're done at the airport, go directly to your hotel, and go to the front desk. They'll let you know if your room is ready or not, and if not (a fair assumption), they'll store your bags. Then just take a walk, go to a bar (a cafe, in other words, but Italians call them bars), get a coffee or whatever you want to drink, and relax.

Thanks for all your great suggestions and encouragement! I am looking forward to my morning visit to a cafe/bar, I'm sure I will need a strong coffee by the time I arrive!

We stayed in Trastevere this summer and needed a breakfast hangout spot after we checked out of our apartment near Dar Poeta and before we took a taxi to the airport. Depending on where in Trastevere you are staying you might want to look at Meccahismo Bistrot near Piazza Trilussa, Ponte Sisto and the neighborhood taxi stand.

If this location isn’t near your accommodation just do what others have suggested in looking at Google maps for an eating place near you. It’s a bit tricky because ours advertised itself as a bar and bistro but it was open from 7:30 AM to 2 AM and served a great breakfast in a nice place to hang out for an hour or so of a morning. We didn’t eat any other meals there. Enjoy your time in Rome!