The palace can be toured.

The attached map overlay:

Schönbrunn (Vienna) palace and gardens map
This map shows buildings of major public interest, garden partions, alleys and the main entrances used by visitors, but omits smaller objects like monuments and paths. It was created by mergeing officially available maps, mainly Google, as well as satellite photographs. The darkest and grey shades mark areas of restricted or no public access. The brightest green shades mark "parterre" arrangements, and a medium darker green was used for areas which were converted into "English style" garden, like the Botanical Gardens (20), mainly in 1830-1848. Brown shades mark areas where a fee is requested for access. The darker brown marks part of the "Tirolean Garden" which now belongs to the zoo.

As of now, the characters and numbers mean the following:

• I – Haupteingang - Main entrance, the official's way to arrive. Would be used if you'd arrive by tourist bus.
• E – Besuchereingang für Schlossbesichtigung - Visitor's entrance to Imperial rooms.
• M – Meidlinger Tor (gate), as accessed by underground U4 station Schönbrunn.
• T – Maria Theresia Tor (rather used by locals only)
• H – Hietzinger Tor, as accessed by underground U4 station Hietzing, which is the usual approach for visitors of the zoo or the palm house.
• X – Maxingtor (rather used by locals only; not open every day)
• Y – Tiroler Tor (rather used by locals only; not open every day)
• Z – Zoo

(1) - 'Wagenburg', ehemalige Winterreitschule, jetzt Museum für Kutschen - 'Wagenburg', a carriage museum.
(2) - Theater - Theatre
(3) - 'Orangerie'.
(4) - 'Reservegarten' (Glashäuser, nicht öffentlich zugänglich) - (greenhouse area, no public access in general)
(5) - 'Kronprinzengarten' ('Privy' or 'Crown prince's' garden).
(6) - 'Großes Parterre' - Great Parterre
(7) - 'Neptunbrunnen' - Neptune Fountain, between the palace and 'Gloriette'.
(8) - 'Gloriette'.

(9) - Obeliskbrunnen - Obelisk Fountain.
(10) - Engelsbrunnen - Angel's well.
(11) - Der 'Schöne Brunnen' - The 'Beautiful Well' which gave the name to the place.
(12) - 'Römische Ruine' - 'Roman Ruin'
(13) - Rundbassin - Round Pool
(14) - Taubenhaus - Columbary
(15) - Irrgarten - Maze
(16) - Sternbassin - Star Pool
(17) - Rosarium - Rose Garden
(18) - Palmenhaus und Palmenhausparterre - Palm house and its 'Parterre'.
(19) - 'Sonnenuhrhaus', jetzt Wüstenhaus - 'Sundial House', now Desert Experience House.
(20) - Botanischer Garten und Altes Palmenhaus - Botanical Garden and Old Palm House

(21) - Japanischer Garten, links neben dem Haupteingang zum Tiergarten - Japanese Garden, left of main entrance to the zoo.
(22) - Zoo und 'Kaiserpavillion' - world's eldest existing zoo, with 'Emperor's pavilion' (now a Café).
(23) - 'Tirolerhaus' und 'Tiroler Garten', now part of the zoo. 'Tirolerhaus' restaurant is outside the zoo. Side entrance to zoo (open temporarily).
(24) - Bundesforschungs- und Ausbildungszentrum für Wald, Naturgefahren und Landschaft (BFW) - Federal Research and Training Centre for Forests, Natural Hazards and Landscape - formerly Forstliche Bundes-Versuchsanstalt (FBVA)
(25) - Höhere Bundeslehr- und Versuchsanstalt für Gartenbau
(26) - 'Kleine Gloriette' - 'Little Gloriette'
(27) - 'Schönbrunner Bad' (a public swimming pool).

(28) - 'Meierei', now a restaurant.

Schönbrunn Palace

Schönbrunn Palace (German: Schloss Schönbrunn [ʃøːnˈbʁʊn]) is a former imperial 1,441-room Rococo summer residence in modern Vienna, Austria. One of the most important cultural monuments in the country, since the 1960s it has been one of the major tourist attractions in Vienna. The palace and gardens illustrate the tastes, interests, and aspirations of successive Habsburg monarchs.

• http://en.wikipedia.org/wiki/Schönbrunn Palace
• Hillman 1000 Wonders