I am familiar with the St. Wolfgang area. There are plenty of summits in all levels of difficulty nearby.
You are based at the foot of Schafberg, OE/SB-216. This is a three hours hike from St. Wolfgang and all exposed to the sun. So not the best target for August. You might consider the cog railroad as an alternative which will bring you close to the summit. It is a bit pricy though! https://www.schafbergbahn.at/content/website_schafbergbahn/en_uk/timeprice/sbbprice.html I would go early in the morning. This summit is overcrowded when the weather is fine. Views are excellent and this is a good VHF site.
In St. Gilgen there is Zwölferhorn, OE/SB-257. A cable car can bring you almost into the activation zone. This is probably the best compromise of easy accessibility, a good view of the area and SOTA possibilities. Food and drink is available in the summit area.
At the east end of Lake Wolfgangsee is Bürgl, OE/OO-428, which is a nice walk of about one hour. The last section to the summit is without a marked trail and at this time of the year probably overgrown. There are gps tracks on SOTAmapping.
A nice walk from Bad Ischl is Jainzen, OE/OO-320, which has two marked trails to the summit which can be combined to a loop. Tracks are on SOTAMapping.
There are many more options. I would need to know if you have a rental car, how far you are willing to drive and what your comfort zone is for elevation and eventual climbing to give more specific recommendations.
Enjoy your time in Austria!
73 Heinz, OE5EEP