The 3 day itinerary of Vienna in the Destinations section of the Fodor's website is good:
On our first morning in Vienna we did a half-day introductory tour with Vienna Sightseeing Tours ( www.viennasightseeingtours.com ). The tour took us on the Ring Strasse, the road that circles the Innere Stadt (the city core). As we drove along, our guide pointed out major landmarks. Then the tour took us to Sch��nbrunn Palace, which is a bit of a distance from the Innere Stadt. We loved Sch��nbrunn, and the temperature was fine when we were there in September. However, our guide did tell us that Sch��nbrunn was not heated, so people who visited it in winter needed to dress warmly. Anyway, we felt that the introductory tour gave us an efficient overview, and we thought it helped us to use our short time in Vienna effectively.
Stephansdom (St. Stephen's Cathedral) in the heart of Vienna is a must. We also very much enjoyed Karlskirche (St. Charles's Church). If memory serves me correctly, Karlskirche was the one significant attraction we saw that wasn't included in Fodor's suggested itinerary. We were glad we made the effort to see it. The Belvedere Palace, which is now an art gallery, is another must.
Vienna has an excellent public transportation system. However, with the exception of Sch��nbrunn, we found that everything we wanted to see in Vienna itself was in walking distance of our hotel, which fortunately was centrally located.
Friends who previously had been to Vienna, Budapest and Prague told us that Vienna, having been the capital of the empire, was very grand, and that it had an "air" about it even to this day. From these friends' accounts I had gained the impression that the Viennese people might be snobbish. I found that not to be the case at all. In fact, we thought they were very friendly. But it was true that the BUILDINGS in Vienna were on a larger scale than their counterparts in Budapest and Prague.
Get ready for sticker shock in Vienna. Your Aussie dollar will feel like Monopoly money. Well our Canadian dollar certainly felt that way to us. We passed a store window in which there were teddy bears and similar toys. The price tag on a stuffed elephant, about 30 cm (1 foot) high, was 519 EUR! However, we did manage to find restaurants and cafes that were not outrageously expensive.
Expect daily highs to be around 14 deg C (although they could range from freezing up to 18 or 19 deg C). Daily lows in early April average 5 deg C, but on occasion do go as low as - 3 deg C. You have about an even chance of encountering rain, and a SLIGHT chance of encountering snow. I don't know where you live in Australia, but if you know what the Blue Mountains are like in winter, I would say you might take clothing that would equip you for that and you'd be okay in the Central European spring.