I've hesitated to add my hideaway to the list because it is always so calm and peaceful. you can read there for hours or observe the people outside chasing the tramways 60, 10 or 58, the underground or all the different busses going into the depths of hietzing.
it is a good thing to begin the day with a breakfast at wunderer with a frehsly squeezed carrot-apple-juice and "resch kaisersemmeln". as it is also a restaurant you get fresh menus there but my favourite is the traditional kärntner speciality "kasnudeln", which are some kind of round molded noodles filled with a mixture of potatos, cheese and mint, covered with brown butter and served with a firm salad. for me they serve the best ones in vienna.