In response to suggestions by several of you, we have rented an apartment near the Statsoper. We plan to take the train from the airport and I am assuming we will need to also catch a UBahn to get to our apartment. I have checked a Vienna map and a travel book, but can't get a clear idea of how we do this. It appears we need to catch the Westbahn train. Correct? Is it easily located at the airport? And then which UBahn from the train station?
We have used public transportation in many European cities and have found there are often tips to be aware of which make getting on the correct line, going the correct direction easier. Are there tips for using the trains and UBahns in Vienna? We also plan to do a day trip to Melk and Durnstein.
Thank you.

Take the S-bahn from airport to Wien Mitte (Landstrasse) station, from there I believe you take the U-bahn (U4) to Karlsplatz. That should put you where you want to be, if not you can hop a tram,1 or 2, from Karlsplatz, both circle the Ring. Only buses go from the airport to Westbahn. If you are staying 3 days buy the 72 hr transit pass, a good value which lets you use all the excellent public transit in Vienna...don't buy the Vienna card, not worth it.

Do you have any information about using Taxi/Shuttle from the airport to Stephansplatz?

Our hotel is very near.

Taxi should run around 35 euro, without tip. You can also take the s-bahn to Wien-Mitte (Landstrasse) station and from there take the U-bahn, line U3 which is about 2 stops from Stephansplatz. I recommend taking the public transit, the s and u bahns are extremely efficient and very reasonable. DO NOT take the special City airport train (CAT)it is more money and not that much faster than the regular S-bahn. Where do you stay in Wien? Is it your first visit?

Thanks for the quick response.
No, it is not our first visit. We had some difficulty in booking this time as our normal hotels were booked.
We were recommended to the Pension Pertschy. We have not been there and hope that it is OK.

From all reports I hear the place is great. We usually rent an apartment; a great value and wonderful experience as well. From your stop at Stephansplatz (assuming you are taking the u-bahn) walk up the Graben (away from Kartnerstrasse) and Habsburgergasse is about 4 blocks up on the left...Pertschy is house #5 and I believe the pension itself is up a few floors.