Inside the Hofburg palace premise, from the main courtyard, you have to enter through a tunnel. Just look for signs to the Schatzkammer, taking you to a smaller counrtyard. The Hofburg Treasury is located at the right-hand corner.
Inside, you can buy a combo-ticket for both the Treasury and the Kunsthistorisches Museum, saving some euros, if you plan to see both places. Admission includes a basic tour audioguide, giving commentary on some of the treasures. For a more extensive audioguide, it will cost additional 3 euros. It'll depend on your interest level.
The Treasury contains the royal jewels of the Habsburgs and the Holy Roman Empire, showing off the wealth and glory of their empire. Some highlights include coronations, the crown of Rudolf (from the Holy Roman Empire) and a "unicorn horn", which is actually a tusk of some animal.
Some objects are just so nice to look at, and the audioguide does give an informative and interesting commentary, telling the history of the jewels. Better than I can give it here in this review.
Photography is allowed, but since the lighting is dim, the photos may not come out right, as you will see when looking at some of the photos I took.
Definitely more interesting than the Porcelain Collection in the Imperial Apartments, and worth checking out.
This review is the subjective opinion of a TravelPod member and not of TravelPod.com.