I don't often do trip reports, but do share the aspects of coming and going, so ...
I have a 6am flight to AUS so about 16 hours ago I used the City Taxi App to set up the taxi to the airport. My impression of the app is that it's not a reservation, but it puts your request in the system about 30 min prior to pickup, and whatever taxi is free, responds. With that in mind, and it being Friday, I requested 3 hours prior to flight time just to have a little buffer. I don't sleep anyway, so it doesn't matter.
The taxi arrived 15 minutes early, so I am way early. Cost was 11300 forunts from about the Opera House. Took 35 minutes.
Went straight to security as I am carry-on only. I dont have a hangup on traveling light. I just dont like waiting in ticket counter lines. Everyone else will need to wait until at least 4 am.
Most EU flights depart 2A, but 2A security was stiĺl closed, so I walked past the few dozen people who were waiting, and I walked down the hall to 2B where security is always open. Both dump into the same departure hall, so it doesn't matter. Took 5 minutes to pass through security laptop and liquuds out and shoes on. The agents were kind and helpful with everyone. One perfectly legal hard sided spinner and one backpack legal on Lufthansa because the only thing in it are a laptop some meds, liquids and my keys so it will scrunch down to the Lufthansa 4" maximum thickness. My carryon is half empty, so I might cram it inside of it before the flight. Also, a small cross body pouch that hangs at my hip for the cell phones, passport and wallet. Empty pockets, watch is packed.
Then straight to the rooftop terrace to watch the planes come and go. Not many this early. Where I am comfortably sitting now. About 4:30 my favorite restaurant wilĺ open and I will have breakfast. Most open at 4am.
Now at O'Leary's for breakfast. Full English breakfast about $12 and its enough for 2. Americano coffee is about $2.75. Expensive for Budapest but cheap for airport food. In front of me is a flight board so I can see when my gate opens.
So far, stress free.