by train to Vienna, Vienna

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At the moment the cheapest way from Vienna to Budapest is by bus, Orangeways from Praterstern / Nordbahnstrasse 50 via Vienna airport to Üllõi út 129, FTC Stadion, Budapest, with online booking 3300 Forint, or with Volanbusz from 2900 (from the Volanbusz terminal Üllõi út 131 to Vienna Erdbergerstr. 200a bus terminal, it is the same bus as Westbus or Blagus, but € 19 from there website).
You can also get in Budapest a 4 day return ticket for € 25 / 7250 Forint (same as single ticket, 13*** Forint for 30 day return) by train, no advanced booking necessary. Most trains to Vienna leave from Keleti puc station and go to Wien Meidling, many also to Wien Westbahnhof. From Vienna at the trainstation € 36 and with advanced online booking from € 19 for a single ticket.
http://www.elvira.hu/index.php (only the hungarian page gives prices, don´t book online with them unless you live in Hungary!)
http://www.oebb.at/en/Travelling_abroad/SparSchiene/Hungary/index.jsp
http://www.orangeways.com/en
https://westbus.at/en
Read more: http://members.virtualtourist.com/m/p/m/200552/#ixzz1vfaE4i44

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Trains to Salzburg leave from Westbahnhof (trainstation), there are now 2 companies:
Oebb € 19 with advanced online booking but you can´t change the train, 47,50 if you buy the ticket at the station. Railjet, 2.45 hours, every hour 14 minutes past the hour, Oebb IC 3.05 hours, every hour 44 minutes past the hour.
Westbahn €23,80, weekends € 14, buy the tickets in the train or online. 2.57 hours, every hour 31 minutes past the hour.
http://www.oebb.at/en/Travelling_in_Austria/SparSchiene_Austria/index.jsp

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The old Südbahnhof is replaced by the future Central Station, until that is finished:
Trains to Roma, Milano, Zagreb, Warsaw, Praha, Ljubljana, Klagenfurt and Graz leave only from Wien Meidling.
Trains to Bratislava from Südbahnhof Ost (temporary station a bit east of the old Südbahnhof).
Trains to Budapest leave from Westbahnhof via Wien Meidling to Budapest (Keleti pu).
Trains to Venice in the night from Westbahnhof, daytime until Villach from Wien Meidling, then by bus.
Westbahnhof for trains to Munich, Zürich, Frankfurt, Paris....

City Night Line is a very comfortable night train. You can book a reclining seat, a couchette or a complete bedroom. We had booked the reclining seat, it was a lot more comfortable that for example a seat in a plane. Pillows and blankets are provided. Since the train only stops in some stations to let people on or off, you get a few hours uninterrupted sleep at night. The conductors make notes where people want to get off and come to wake them in the morning.
You save a night in a hotel and you can save a lot a money, if you book one of their specials. We paid 29 Euro each, now - February 2006 - they have an offer for 19 Euro.

The City Airport train leaves at 07 and 37 minutes past the hour - a return ticket is EUR 15 and takes you to Wien Mitte (Landstrasse). The service is comfortable, but pricey. A cheaper way is to get the Schnellbahn (EUR 1.50 to the edge of Vienna and then a daily/weekly/monthly pass will cover the rest of the journey for free).

Train tickets from Budapest to Vienna are 9860HUF pp or approximately 36euros pp. The ticket is also good for 2 days of public transport in Vienna upon arrival which I thought was a good addition although I don't know if the same applies if one is going to Budapest from Vienna. I wouldn't buy my tickets online instead I bought my tickets the day before I left. Trains leave every 2 hours from Keleti Station, which is on the M2 line of the Budapest metro. The train stops at Vienna Meidling and Westbahnhof stations. The train ride is approximately 3 hours.

I spent ages trawling the internet for a way to buy train tickets to Vienna in advance and have them posted to my home in the UK without any luck. A friend mentioned the Czech Railway Tickets website, where you can book online. You don't need to navigate foreign websites or complicated journey planners. The timetable is there to browse and you can book in a few clicks. The price was reasonable and my tickets arrived in the post just a couple of days later. I'd definitely use them again.

The best and cheapest way to get from the airport is with the regular (S7) train and NOT the CAT. There is no real advantage to the CAT. When we were there (July, 2010), the train cost 3.60 one way per person whereas the CAT cost about 10 Euros. The CAT advertises a 16-minute non-stop trip in 1st class conditions. Big deal. The S7 is just as frequent and takes half an hour and stops a few times along the way. IMHO, not worth the triple price.