We are arriving mid-morning by train from Melk to Vienna. Am I right in assuming that we will be arriving at the Westbahnhof station? I would like to stay overnight near the westbahnhof before departing for Vienna airport next day. Are there trains from Westbahnhof that go directly to the airport? I am so confused about all the train stations in Vienna.
Thanks for your help.

Trains from Melk arrive at Westbahnhof, but only buses depart from Westbahnhof to airport. Vienna City airport train depart form Wien-Mitte on U3 line. For train schedule, please check: www.cityairporttrain.com.

Perhaps it won't be necessary to stay around Westbahnhof (not the most interesting part of city), if you like old town, as long as somewhere near Line U3, it would be still quite convenient for access to airport.

Thanks JudyC, I appreciate your response.

You can stay at the Fuerstenhof, which is right across the square from the Westbahn. We have stayed there and have really enjoyed the old world charm of the place. Staff is excellent, rooms are wonderful, and the breakfast buffet is very good. Here is their web address: http://www.hotel-fuerstenhof.at/
I believe they still offer a 10% discount for internet booking.

I forget to mention that you are only a 10 minute u-bahn ride from city center if you stay at the Fuerstenhof.