If you can not decide which museum to go here are informations about some of them;

Technical Museum

The Technical Museum recently reopened after renovations. Exhibits from engineering, technology and industry are once again on view. To name just a few: the famous Ettrich Dove, which is still able to fly; steam engines, the bordeaux-red Lohner Porsche, the functioning exhibition mine in the basement...
These flashes of inspiration of the past have been augmented by technical achievements of the present, such as a computer tomograph or a television directing console. And there are plenty of hands-on experiments that appeal to adults as well as to children.
Technical innovations can also seen outside the museum: this mansion from the year 1913, which was built to complement nearby Schönbrunn Palace, features a new entrance hall on the basement level.
The familiar appearance of sumptuous neo-Baroque and Art Nouveau now contrasts with sober additions of glass and aluminum.

Imperial Palace - Hofburg

The Imperial Palace was the residence of the Habsburg emperors until 1918. Originally a medieval castle, of which only the chapel has survived to this day, the residence of the court was expanded and made ever more lavish as the power of the Habsburgs grew and the territory of their dominions increased.
Today, the Imperial Palace houses the offices of the Austrian president, an international convention center, the chapel where the Vienna Boys' Choir sings mass on Sundays and religious holidays, the hall in which the Lipizzan stallions of the Spanish Riding School perform, various official and private apartments and several museums and state rooms which are open to the public.
The New Palace (Neue Burg) is the most recent and, at the same time, most monumental section of the Imperial Palace. It now houses the Ethnological Museum, branches of the Museum of Fine Arts: the Ephesus Museum displaying art from classical antiquity in Asia Minor, the Collection of Arms which ranks as the second-largest in the world and the Collection of Historical Musical Instruments

Museum of Fine Arts

The Museum of Fine Arts was built from 1872 to 1891 after designs by Gottfried Semper and Karl von Hasenauer. Like the second great museum at Ring Boulevard, the Museum of Natural History, it was built as a repository for the vast collections then owned by the imperial family.
The Museum of Fine Arts ranks among the richest and most important art collections in the world. At the core of the museum’s unique Picture Gallery are paintings by Bruegel, Rubens, Rembrandt, Vermeer, Dürer, Raphael, Titian and Velazquez, as well as the most comprehensive collection of Bruegel’s paintings in the world.

Museum Judenplatz Vienna

Judenplatz is considered a singular place of remembrance; it combines three things: Rachel Whiteread's Memorial, the excavations of a medieval synagogue and a museum about medieval Jewry; together they form a unique unit of remembrance.
Floor tiles around the memorial contain the names of the places where Austrian Jews were killed during Nazi tyranny.
The focal point of the Museum Judenplatz Vienna, which is run by the Jewish Museum of the City of Vienna [>], are three exhibition rooms on medieval Jewry in Vienna and the excavations of a medieval synagogue. Here, one can learn about the religious, cultural and social life of Viennese Jews in the Middle Ages, until they were driven away and destroyed in the years 1420-21, the so-called “Vienna Geserah”.

Museum of Military History

The Museum of Military History, designed by Theophil Hansen and Ludwig Förster, lays in the center of the Arsenal (Armory, built from 1849 to 1856). Its collections give a thorough and detailed overview of the development of Austrian military life since the beginning of the 17th century.
Outstanding exhibits include the automobile in which Archduke Francis Ferdinand rode and the uniform he wore when he was assassinated at Sarajevo in June of 1914 (the event touched off World War I) and an excellent display dealing with the Austro-Hungarian navy.

The Essl Collection

Klosterneuburg near Vienna is offering the new museum of the Essl Collection, the largest private collection of contemporary Austrian art.
Heinz Tesar's eye-catching building adjacent to the Danube water-meadows is exhibiting 400 works from this collection of Austrian painting, sculpture, photography and video art since 1945, supplemented by European and American art from the same era.
Stars like Arnulf Rainer, Hermann Nitsch, Franz West, Siegfried Anzinger and Hubert Schmalix are represented with a large number of major works. The group of "internationals" ranges from Georg Baselitz,Gerhard Richter and Antoni Tàpies to Jenny Holzer and Cindy Sherman.