Don't overlook the small but elegant "marble palace" built near the Kaiservilla for Empress Elisabeth, who used it as a teahouse; this now houses a photography museum. The permanent collection offers an interesting overview of the history of analog photography, with a nice tribute to Empress Elizabeth. The marriage between Franz Josef and Elisabeth was not an especially happy one; a number of houses bearing women's names in Bad Ischl are said to have been quietly given by the emperor to his various lady friends (such as Villa Schratt given to Katharina Schratt, the emperor's nearly official mistress). You'll first need to purchase a ticket to the museum to enter the park grounds.
Kaiserpark, Bad Ischl, A-4820, Austria