Firstly No visit to Vienna is complete without a visit to the famous Vienna coffee house Schwarzenberg.
'The history of Viennese coffee house culture goes back to the year 1683, when Turkish spoils of war in the form of bags of green beans came into the possession of a spy and coffee became the favourite drink of the Viennese. Gradually, establishments under the name of Viennese coffee house were opened up and became a popular meeting place.' https://www.cafe-schwarzenberg.at/en/
At historic cafe Schwarzenberg you can go for just a coffee, for hot chocolate, for lunch and/or for dinner. It is always full. If you're clever you'll reserve one of the window tables. If you're not you'll end up queuing outside. Originally built in 1861 - read the full history here - Cafe Schwarzenberg is the best known of all of the coffee houses. It's close to everything cultural from the Staatsoper to the Musikverein and also very close to all the famous hotels and the shopping district. Pay a visit. have a coffee and reserve your table to lunch the next day.
Restaurant Steirereck. No 10 in the list of The World's top 50 Restaurants, holder of two Michelin Stars, you can expect to part with a lot of money here but come away happy. The service, as you'd expect, is superb, the food out-of-this-world delicious and the wines outstanding. Start with a glass of their in house Blanc de Blancs unless you want serious bubbles, then try a delicious Pichler Gruner Veltliner and go from there. This is one of the best restaurants I've ever been to and well worth a visit.
Finally a restaurant that I visited once on this trip but if I went to Vienna again I would definitely go more than one time. Restaurant Paul, at Johannesgasse 16, 1010 Wien, is a restaurant I can definitely recommend. The food is excellent as is the service and you can drink superb Austrian wines that won't break the bank.