The big question - "How to get from the airport to the city" had a simple answer. Bus, train (slow), train (fast), taxi. The least expensive is the slow train that has a station right at the airport. It connects to the metro station at various points in town (about 40 minutes ride) which then spread out all over the city. The CAT is faster (about 16 minutes) as it doesn't stop along the way, and also connects to the metro at the end of the line.
Vienna is a cyclist's city, with bike paths set in the sidewalk. I didn't know this and paused smack in the middle of the bike lane to look at my map and set a cyclist madly ringing his bell at me. Unfortunately deaf to such things, I didn't budge and he had to swerve around me. I must have been like Mr. Bean, walking obliviously away after creating havoc at a scene.
Vienna Metro Map - See how to get around. Vienna gets a A++ for public transport.
Vienna Metro ticket options - Vienna website with hourly, daily, weekly options.
Their transportation system seems to run on the honor system as there are tickets on sale, but no one to check to see if you bought them or gates to go through. No one ever checked our train ticket and the bus driver claimed to not have any more tickets and let us ride for free.