I have a question for those of you familiar with Budapest. We have two nights post river cruise in Budapest the third week of Sept. Our flight leaves at 6AM (most crowded time at that airport), so we will need to be at the airport at 3AM. Would you advise staying near the airport and taking transportation into Budapest each of the two days, or would staying in the city and leaving for the airport an hour earlier to make our trip richer? Extra points for hotel suggestions. Thanks.
Easy, answer.
I take a 6 to 6:30 am flight out of Budapest 4 times a year. Yes, it is among the more crowded times but not horrible. The airport is rated one of the best in Europe and is fairly easy to navigate and fairly well run in general (https://www.schengenvisainfo.com/news/airports-council-international-awards-budapest-airport-as-best-in-europe/#:~:text=Budapest%20Airport%20has%20been%20awarded,world's%20leading%20passenger%20satisfaction%20survey).
I wouldnt show up until 3:30 am and I do that because i am personally paranoid about such things ... most will tell you that 4 am is fine and they are probably correct. Taxi time to the airport from most of "tourist" Budapest at that time in the morning is 40 minutes. Cost is about 12.000 forints. My prefereed taxi company is City Taxi (book 24 hours in advance).
To your question. Get a hotel in town. For two nights my preference would be on Pest side, and on the river or second choice on lower Andrassy ut so you get the most out of the limited time you will have.
For more detail, look at my 07/19/23 post here: https://community.ricksteves.com/travel-forum/hungary/keleti-station-to-the-marriott
I would stay in the city to maximize your time and to avoid another pack-unpack-pack at a hotel. Mr. É's post will provide several good options, but just to make sure I get a few points, Hotel Moments always has rave reviews and is in an excellent location. ;)
The check in counters don't open until 2 hours before departure, so you'll be standing around for an hour if you arrive at 3. The airport is busy at that time, but it's never terrible. We typically arrange a 3:30am pick up and always have time to have breakfast in the lounge before departure and never feel rushed.
On an April visit my wife and I liked the Prestige Hotel in Pest a lot. We did also stay a night at the Ibis Styles Budapest Airport before an early flight. It is right next to the terminal and serves its purpose of convenient airport hotel very well (they know their market -- breakfast was served starting at 4 am!). However, ours was a split itinerary, where we spent a few days in Budapest (at Prestige), then went to Vienna, then came back to Budapest the evening before our flight, just for that one night. So it made sense for us to stay that night at the airport hotel, and I do recommend the Ibis for those who want that, but I agree with the other commenters that with your itinerary it would be best to stay both nights in town.