I've put it into AI and it's suggested Hall in Tyrol or Alpbach, Mühlbach am Hochkönig, or Saalbach which is apparently gentler
I live in Austria and know all of those areas. Hall in Tyrol is not suitable - quite a distance from the mountains really, it's just a small town in the Inn valley. It's quite nice but not really for kids.
Alpbach is very beautiful, lots of mountains, great for hiking but very upmarket and not a lot to do in the village especially with children.
Mühlbach is quite out of the way. I assume AI came up with it because it has a marble run (I'd not heard anything about marble runs here so they must be a relatively new trend as I can see a few places have them now that I've googled). I wouldn't go to Mühlbach.
Saalbach is the best choice of the AI suggestions. I don't know why it said it's "gentler". Heavy duty hiking to be had there. However, it is very nice and very well set up for kids. The marble trail is in Viehofen just down the road and accessible by bus. You can get to Saalbach from Salzburg Airport with one change of bus. If you do decide to go there and need any help with bus timetables at a later date do let me know as I can help you.
https://www.saalbach.com/de/sommer/familie
I'd recommend Zell am See which others have suggested. It's a beautiful setting. There are cable cars and the view is spectacular. It's easy to get to by a direct bus from Salzburg airport. You can swim in the lake and there are 3 lidos with things like slides and inflatables. If the weather is shite there's an indoor swimming pool which is nice or you could get the bus to the Tauern Spa at Kaprun. Again, if you decide to go and want some more tips, let me know.
You could go to one of the villages in Salzburger Saalachtal https://www.lofer.com/en/things-to-do-in-summer/family
Accessible by bus (the Zell am See bus) from Salzburg airport, takes about 45 minutes. With guest cards the bus is free as are all local buses, the cable-car, the swimming pools, the gorges etc. and there's a bus from the village of Weißbach into the mountains on the border with Germany with lots to do including a parcour and a low-ropes course which your kids might like. The Seisenbergklamm (gorge) in Weißbach is spectacular. Vorderkaserklamm is also nice. Outdoor pools in Lofer and Unken.
The Almenwelt Lofer is nice https://www.skialm-lofer.com/en/summer-in-lofer and lots of easy hikes including one to a peak Grübhorndl which gives you a spectacular view of the mountains.
Neustift in Stubaital is also really nice. Lovely valley, lots to do. Accessible by bus from Innsbruck. Flying into Munich works as well as you can take the train and then the bus. There's the Stubai glacier at the end of the valley and you can take the lift all the way up to the top for spectacular views and snow! www.stubai.at
Or you could go to Maria Alm https://www.hochkoenig.at/en/family-holiday/family-summer-in-the-hochkoenig-region.html which is part of the Hochkönig region where Mühlbach is. Very beautiful place. You'd need to change bus from the airport (change in Saalfelden) but that's easy to do. And then you could go on the bus to the marble run in Hochkönig.
If your kids are set on the marble run you could access the one at Viehofen by bus from Saalbach, Zell am See, Saalachtal or Maria Alm.
Saalfelden (also accessible from those 4 places) has a summer alpine coaster which the kids might like.
Plenty of ideas for you. Feel free to ask if you want to know more or need any tips.