The rail transfers at both ends (especially in Budapest) are awkward.

In Vienna, from the airport, take the local train (not the CAT airport train) to Rennweg (about 20 minutes; trains generally run every half hour in daytime). Cross to the other side of the same platform, and take any train (except to Flughafen/Wolfsthal) to Meidling (about 10 minutes; frequent trains). At Meidling you need to change platforms (easy) via the lower-level concourse to catch the RJ to Budapest.

This is a bit frustrating because Vienna airport is on the Budapest side of the city, and the rail lines to Budapest and the airport almost kiss several kilometres to the south-east of the centre, so there is some unavoidable backtracking involved.

Alternatively, there is a Vienna Airport Lines bus from the airport to Meidling which runs half-hourly and takes half-an-hour.

The train fare (airport to Meidling) is €4, while the bus fare is €8. Taxis in Vienna are expensive.

In Budapest, if you are transferring from the RJ directly to the airport, it gets more difficult. Take the train to the terminus, Keleti. Unfortunately, the trains to the airport leave from Nyugati station, which is not far but a bit tricky to get to (by a combination of bus and tram, or changing lines on the metro). The airport station (Ferihegy) was built only a few years ago next to Terminal 1, which is now closed. Terminal 2 is about 5km away, and reachable by public bus (200E) from the rail station. However, the 200E starts its journey from the end of metro line 3, at Kobanya-Kispest, and is invariably packed by the time it gets to the airport station.

If you want to do this journey by public transport (metro), take line 2 from Keleti station to Deak ter, transfer to line 3 to Kobanya-Kispest, and take the 200E bus as above. Not recommended with luggage, and it will take over an hour.

In this instance, I would definitely recommend taking a taxi. Under no circumstances engage with the touts with official-looking badges who meet every international train – they are con-merchants. Your best bet is to stand outside Keleti station (exit to the area to the left of the main station building as you arrive) and call a cab (don’t take any arriving or lurking cabs). City Taxi is reputable and has helpful, English-speaking operators who will tell you where to wait, what type of car your taxi will be, what its number is, and how long it will take to arrive (generally less than 10 minutes). Ask for the (fixed) transfer fare to the airport – it is currently a reasonable HUF 4,800 – about €18.

As an alternative to all of this, there are bus services direct from Vienna Airport to Budapest (Nepliget, on the airport side of the city and on metro line 3) operated by Eurolines and Orangeways.