Do you know what I would do in your shoes? I would have a coffee at the station, than I would walk to the shopping mall Sillpark (about 5 minutes, on the right exiting the station, right under the railway tracks and you see it in front of you), that opens at 9am. At the second floor on the right there is the Dorotheum jewelry and pawn shop. The jewelry is as good as any one, what is interesting is that small items that were not redeemed at the pawn shop are not auctioned but put on direct sale. It is often possible to find vintage pieces like golden brooches in the 100-200 euro price bracket, in a variety of Austrian designs from the 19th and early 20th centuries. Being a pawn shop you can never tell what the selection will be but a visit is often interesting. Look for "Einzelstücken aus Privatbesitz".
The Golden roof is only moderately interesting. What you get is a walk around the old city center, that is very compact around the Golden roof - for example, the stuccoed home just in front of it is much more beautiful. But a meaningful visit would need at least a 3-4 hours time window. The zone between the station and the historic center is not interesting. The Marie-Theresien-Strasse with baroque palaces on the background of mountains is quite scenic.