Requirements for visiting Hungary for a week? :)

Have a US passport with at least 6 months left on it. Just tell the immigration officer the purpose of the trip and how long you intend to stay. Should be as simple as that.

OK...I was just in Hungary last summer and none of this was necessary. If you have a US passport you simply present it at customs and that's it. I've flown into 8 different countries in the Schengen Zone in the past 4 years and have never been asked for financial statements, employer letters, or anything of the sort. The only reason a customs official would have reason to ask these things of you would be if they suspect you intend to overstay your 90 day limit as an American tourist. That is easily solved by presenting your return ticket to the US...I have never, in 30 years of traveling to Europe, been asked to show a return ticket. I wonder why they questioned you in the UK?
The basic information for this is found on the US State Department Website about entry to Hungary. Click the blue to see it.
David Sedaris has a home in the UK and has a long term residency visa, so his entry into the country as a US citizen is, understandably, going to be a little more complicated than your average tourist whenever he returns there. You really can't compare his experience with what you should expect as a tourist. His stories are funny but not typical!

Thanks for the replies everyone! :)

And Anita, what happened in the UK, he seemed suspicious that I was only there a week. What happened was, he asked for length of visit, and I said a week, and his eyes narrowed and he asked, why only a week? And I said: that is how much time off I can currently take? Then he absolutely started grilling me: he asked me where I was staying, the address of the hotel (which was right next to the airport!), how long I'd been working at my current job, if I had lease for my apartment, how much money I had in my bank account (!)...it was just kinda mind blowing to be honest. Everyone around me went very, very quiet. It was quite humiliating. He was extremely suspicious of all my answers, but what made him relax slightly was when I told him the amount of money currently available in my bank account. I feel very very odd explaining this story, I've never told anyone, too embarrassed.

On the return, my flight was routed through Canada, and I chatted with the Greek-Canadian customs agent for a minute -- I was interested in his name (I am with everyone), and he was nice and delighted in my interest...but then suddenly he shifted into 'security mode' and very firmly/sternly asked me the questions (purpose of visit? ...to connect to flight back home to America? "Are you SURE?" is what I felt he wanted to say).

I figured, it's just how you have to be with the job. You deal with all sorts you know? And, if someone gets through the border at your checkpoint, that's your fault for not being vigilant enough. Better I suppose to be tough with everyone than profile, it was just humiliating, and am now nervous about checkpoints.

And yes to what you said about the suspicion for those who may overstay their visit in the UK -- I figured that's why he was suspicious of me, because I was staying 'only' a week. And, I could see why that'd be a little suspicious, except y'know I'm from a country where paid time off is a luxury and not an expectation! :P

Oh oh oh just wanted to mention too that I know a Brit who's flight (this was 8 years ago?) to California first stopped in Chicago, and he is STILL bothered by how extremely rude and suspicious the US customs lady was. He got the same treatment I did, and felt like she made a loud, embarrassing scene trying to expose him as a foreigner trying to sneak into America forever. He and a friend were visiting a friend who'd moved to America, so I suppose that was the fear there, that he'd just stay forever on his friend's couch...?

Thanks for the tip James, I'm listening to youtube videos as much as I can (while commuting, cleaning etc) for Hungarian phrases :) The few Hungarians I have met in my life praised me (in apparent surprise) at my pronunciation, my mother speaks Hungarian and only ever taught me a single sentence, so can't say I speak it but I'm grateful for even that instruction. My mother was absolutely fanatical about pronunciation, and would say that mispronounced Hungarian was like a cheese grater on the brain -- imagery which made me shrivel up inside but also provided sufficient encouragement to make me pay very close attention to what I was trying to say! My greatest fear is going to Hungary, trying garbled Hungarian and not being understood by the locals. When I'd try Korean in Korea they were SO encouraging and you could tell they WANTED to understand what I said, which just made it all the more embarrassing that I was trying so hard and failing to communicate! And being half Hungarian, I feel like I don't have an 'excuse' you know...? I discussed this with an Anglo-German girl in Korea, about how in the UK and America we (well most people!) are used to hearing English pronounced by a variety of accents, but most languages, they are used to only hearing native speakers speak their language. I love accents of all sorts, but am verrrrry self-conscious of having a 'flat'/'inelastic' American accent if you know what I mean. I think for studying a foreign language, learning first pronunciation is most important, but I am wildly digressing here :P

Also what you say about the 'suspect room' sounds terrifying to me, but you just reminded about a friend of mine who was detained trying to leave Israel because he visited Palestine. He used one of the few Hebrew words he knew (for 'marijuana'), which made the guard laugh and let him go...can't remember the details of the story, but it was very funny, to hear him tell it. This guy is the harmless type, doesn't look 'druggie' at all, very easy-going, but rules are still rules of course :)

Back in the 70's I had a Canadian friend here doing post-grad work in Israel. Every time he went back for a visit he'd let his hair and beard grow for a couple months. He always had to go through US customs then (no direct flights to Canada) He said it was worth the grilling he always got (for suspected drug trafficking coming from the Middle East with his hippie look) to see his parents faces when they saw their usually clean-cut son.

"A justifiable reason for your travel" I have been to Hungary three times since 2010, ie crossed into Hungarian soil, never dawned on me to have a "justifiable reason", had to show my Passport only once, maybe twice on the same trip in 2010. The other two trips in 2014 and 2015 I wasn't even asked. Plus, I was never asked why? I show them the train ticket, not a rail Pass. Of all countries I have traveled in Europe since 1971 as a natural born US citizen with an American passport, only two asked me at passport control time...UK and Holland for the "justified reason" ie, the nature of your business, regardless of how long, 14 days, 30 days or even 67 days in 2009. Certainly not the Hungarians.

If I were to stay in Hungary for a week, very conceivable in the future, with most days staying in Budapest, I would arrive by train, (where the passport could be checked), reserve at the hostel and a Pension, where, of course, you will have to indicate your passport number on the sign in form and show the clerk the passport. No one has ever asked me for a bank statement at any airport I landed be it Gatwick, LHR, Paris, CDG or FRA. I would have said what bank statement? Only once in 1971 at the Dutch-German border on that night train from Vienna did the Dutch ask to see my return airline ticket to Calif.. I had been warned of this and had it on me. They asked about my length of stay. I told them (there were 2 of them) 2 full days, then I'm leaving, ie, I'm not spending any money in your country, pal.

Wow! What a horrible experience you had in the UK! I can see why you've never told that one...crazy.
My worst experience was when I went to Thailand. We were planning to stay the maximum amount of time allowed and I was a bit worried about doing that. At customs coming into the country I was nervous about this and it must have showed. I was pulled aside, taken into a back room, questioned, then taken back out to the custom line and THOROUGHLY frisked. It felt like something from a movie! It all ended up fine but it was nerve wracking!
Nothing like this has ever happened to me in Europe but that doesn't mean it wont.
Just be yourself, relax, act happy to be there, and cross your fingers! I'm sure it'll be fine.

James--I took your advice and ordered the Pimsleur Basic Hungarian CDs and I am having an absolute blast learning some basic words and phrases, thank you so much for the suggestion. I know it's not at all necessary as there's enough English spoken in Budapest for the average visitor to feel comfortable, but I wanted to explore this part of my heritage and it's a really fun way to prepare for my upcoming trip in May. I'll be "jo reggelt-ing" and "koszonom szepen-ing" everyone!