Originally Posted by MichaelA380

At 5pm everything will be crowded but the public transport in Vienna is mostly air-conditioned (100% buses, >50% trams and metro). There are numerous ways to reach the hotel from the airport, it depends on your comfort preferences, price flexibility, timetable, etc. Using CAT + U4 is the most expensive one and not necessarily the fastest one (depending on when you arrive at the train station). Other possible options from the airport:
- S7 / REX7 to Landstraße Bahnhof Wien Mitte + Metro U4 to Pilgramgasse
- RailJet to Wien Hauptbahnhof + Bus 13A to Pilgramgasse


Huth, Figlmüller and Sacher are the typical tourist traps in Vienna - overrated and overpriced - but that is only my personal opinion.
For typical Austrian choices you can also take a look at Plachutta, Schweizerhaus or Melker Stiftskeller - however for all you require a reservation in advance.
A little bit cozier but a personal favourite of mine that all my visting friends and family have enjoyed is Zum Leopold.
Which of these satisfies your amex prerequisites is up to you to verify.