I´m probably a little biased on this site, since I have been there so many (innumerable, practically) times. The World Heritage area is just the Inner City (the First District), plus a few areas besides (like the Belvedere Palace area), but it really captures the essence of Vienna and gives a great overview of its history, from the earliest beginnings as a Celtic and Roman settlement through the (frankly less remarkable medieval and Renaissance periods) to the time of Vienna´s greatest glory, the Baroque, when it was the capital of a huge empire, and on to the 19th century, when the Ring Street with the Parliament Building, City Hall, the University, the Opera, and the two great museums was built. So wandering around the Inner City takes you through all epochs in a short time, and there´s a lot to see, but the major, must-see attractions are St.Stephen´s Cathedral and the Hofburg, the maze-like Imperial Palace Complex. Most impressive is the Treasury, which contains priceless works of art from many periods. Sure, the city can get very crowded, but it´s easy to get off the tourist trail - just don´t take a map and let yourself get lost in the small streets and alleys. Sooner or later you´ll end up on the Ring. And since one of the major reasons for inscription on the WH list was Vienna´s role as a capital of music, a night at the Opera or at one of the many concerts is probably a must as well.