Recently took my 6 year old daughter to the Spanish Riding School in Vienna. Though it was summer and there are no regular performances, definitely a special treat. They run a summer program featuring the young stallions from their studfarm in Piber, near Graz, Austria. In essence, their college team before they start the long formal training at this, the worlds oldest riding academy.
Though very popular, this place is not touristy, just classy.