While I was doing some undergraduate teaching in Germany, I visited the Hofgarten during a weekend trip to Munich.  Unfortunately, I had forgotten that the Hofgarten is mentioned in The Waste Land, and I am currently having difficulty adding photos from my computer to this blog.  However, I think that my personal experience can give a better understanding of what Eliot was trying to achieve by mentioning the Hofgarten.

I think a key part of understanding the importance of the Hofgarten to The Waste Land is its location.  Hofgarten means "courtyard garden," which is very appropriate because it is across the street from the Münischer Residenz, or the Munich Residential Palace.  Every inch of the Hofgarten is extremely manicured, with the plants grown in a precise geometrical pattern.

From the ground (looking a lot better than when I visited in February.)

From above.

This neatness, contrasted with the open, comfortable roughness of the nearby Englischer Garten ("English Garden"), leaves the impression of a luxurious and insular aristocratic life (supported by the stanza's speaker referring to the Archduke as "my cousin" (line 13-14)) prior to World War I.  This gentility, however, was disrupted by the violence of The Great War and the consequences of the Treaty of Versailles.  

I believe that through mentioning the Hofgarten, Eliot is trying to evoke a sense of what life was like before the war, in order to show the disruption it caused.