All three Starwoods (Goldener Hirsch, Hotel Jagdhof, Schloss Fuschl) are very nice.
There is also a Sheraton, which I have not seen.
The two outside hotels (at Fuschl See) are a little far, about 30 min or so by car.
But beautiful scenery ...
Where to book? Try Starwood and some "discount" websites: Expedia, HRS.com ...
Your family will like it ...Salzburg is great. BTW, not far from Fuschl See is Wolfgang See, worth a trip.