Nice, I was on Habicht in July - for one day it really drags, but between Gschnitz and the summit there's more than 2000 m elevation difference. Maybe I'd just comment a bit on the slightly overstated statement: "Habicht is (...) the most visited mountain in the Stubai Alps" - it really is hugely popular, due to its majesty they long believed it was the highest mountain in Tyrol, but after visiting it still lags quite a bit behind e.g. Serles, Nockspitze or Hoher Burgstall, i.e. lower, easier and especially faster accessible viewpoints... The Stubai Alps are, except for more remote areas like the Alpeiner Mountains, due to favorable starting points, numerous cable cars, attractiveness and proximity to Innsbruck extremely popular. I have to admit, the Innsbruck hut under Habicht left the least pleasant memory among this year's huts (and not just because of the proverbial Austrian coolness and apparent soullessness - a short escape to Switzerland was like entering a new world in that regard).
But regarding the view, one can only agree. I wrote about it then: "The view from the summit is almost indescribably magnificent. Due to its height and exposed position, Habicht is the leading viewpoint over the Stubai Alps, which we can almost fully embrace with our gaze, as well as the glacial expanses of the Ötztal Alps, the Ortler group and the peaks of the Zillertal Alps; deep below us are the Stubai valley, Obertal valley and Oberbergbach catchment, the view reaches all the way to Innsbruck and the Karwendel mountains above it. Perhaps the most beautiful are the views towards the bold and attractive Tribulauns, into which I immediately gazed and imagined a tour for sometime next. The best view of them (or them, there are supposedly three) is from the pleasant Alfaier lake, located a little below the path to Habicht.
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That's all about Habicht. Otherwise you've certainly chosen an interesting journey; maybe it's worth mentioning that near the western border of Tyrol lies the more famous Hoher Riffler, which is just over 60 m lower than the Zillertal one and represents the highest peak of the important Verwall range.
Safe steps forward,
Gašper