Budapest is probably my favourite European city - we went for the first time a few years back and loved it so much we ended up going 3 times in a year! Absolutely tonnes to do from family friendly stuff to the ruin bars and it's still all relatively cheap too which is a big bonus. Despite having been a few times now I still feel there's loads left to do there as well, and will certainly be back again soon.
Not one for December but the RedJet boat trips are amazing- high speed 360 degree spins and other nonsenses like sudden nosedives into the water, it's like no other boat trip I've ever been on, full-on crazy stunt action. You will get SOAKED though so it obviously only runs in warmer months.
The pinball museum is a must if you have any interest in pinball at all - hundreds of machines (and some other types of games) all on freeplay, covering the very first machines up until recent stuff.
We hired a car last trip to see a bit more of Hungary, and stayed at a friends apartment in Balatonfoldvar and had great fun exploring Lake Balaton. Really nice to see a different side of the country but again that's one for another warmer visit.
Public transport is brilliant, cheap and easy. From the airport there's a shuttle bus (100) which you pay separately for. For general travel you can get individual tickets valid on the metro/buses/trolly buses or a 3 or 7 day pass. If you go for individual tickets remember you have to validate it in a machine or you might get a big fine (this catches loads of people out and yes, we did see people getting fined for it). getting around is really easy and everyone speaks English and is really helpful.
Various bits we've done on visits:
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Szechenyi Bath (
http://www.szechenyibath.com/)
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Vajdahunyad Castle (
http://en.wikipedia.org/wiki/Vajdahunyad_Castle)
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City Park (
http://en.wikipedia.org/wiki/City_Park_(Budapest)) - Szechenyi Bath & Vajdahunyad Castle is in the City Park behind Heroes Square
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Heroes Square (
http://en.wikipedia.org/wiki/Heroes'_Square_(Budapest))
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The House of Terror Museum (
http://www.terrorhaza.hu/) - the Museum is on Andrássy Avenue
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Andrássy Avenue (
http://en.wikipedia.org/wiki/Andrássy_út)
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Deák Ferenc Square (
http://en.wikipedia.org/wiki/Deák_Ferenc_tér) - Andrássy Avenue goes into Deák Ferenc Square
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Margaret Island (
http://en.wikipedia.org/wiki/Margaret_Island)
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Parliament + Crown (
http://www.mkogy.hu/angol/eng/tajekoztato.htm)
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Chain Bridge (
http://en.wikipedia.org/wiki/Chain_Bridge_(Budapest))
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St. Stephen's Basilica (
http://en.wikipedia.org/wiki/St._Stephen's_Basilica)
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Buda Castle (
http://en.wikipedia.org/wiki/Buda_Castle)
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Fisherman's Bastion (
http://en.wikipedia.org/wiki/Fisherman's_Bastion)
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Matthias Church (
http://en.wikipedia.org/wiki/Matthias_Church)
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Vörösmarty Square (
http://en.wikipedia.org/wiki/Vörösmarty_Square)
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Váci Street (
http://en.wikipedia.org/wiki/Váci_Street)
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Great Market Hall (
http://en.wikipedia.org/wiki/Great_Market_Hall_(Budapest))
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Citadella (
http://en.wikipedia.org/wiki/Citadella)
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Gellért Hill (
http://en.wikipedia.org/wiki/Gellért_Hill)
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Organic Farmers Market - (
http://bit.ly/oApP9x)
There's loads of great food options to suit all budgets. To be honest I wasn't that impressed with Mazel Tov, a restaurant everyone else raves about but we thought was mediocre on our only visit - maybe we got it on a bad day as the food in the Hummus Bar round the corner on Kazinczy was genuinely better and a lot cheaper.
For ruin bars, Szimpla Kert is the original, on Kazinczy Street, and although it's mainly full of backpackers and tourists now it's still a magic place. About 10 minutes away is Instant, which is even bigger with 6 different bars/dancefloors, again well worth a visit. Also on Kazinczy Street is Ellato Kert, another ruin bar but this one is all open air (so wrap up warm). There's loads of good places here, just stumble around. For great yet cheap sandwiches and soup then Bors GasztroBar is just down from Szimpla.
The only rubbish things I've seen have been thanks to English tourists and stag dos I'm afraid to say. Our Hungarian friend tells me that we don't have a great rep there, and after seeing some idiot with his trousers down waving his little chap whilst having a wee on a war memorial last time I can see why.
On a football related note this is a good read about some of the incredible football stadiums:
The long read: The Hungarian prime minister has been lavishing public money on his favourite sport for years. Could it prove to be his undoing?
www.theguardian.com