We just watched Carmen at the Roman stone quarry in Sankt Margarethen, which is about an hour south of Vienna. It is one of the biggest open air Opera festivals in Europe, similar to Verona. With its unique scenery, which is fully integrated in the performance, it becomes a fascinating experience. Read more here.
Parking is available for free; however, be aware that there is another one charging €10 for the night. Inside the arena food and drinks are available at a reasonable price. Also, there are two backstage-tours available for a couple of Euros previous to the performance. Check the exact times at the link above. There are plenty of hotels around, we stayed in this one, which I can recommend. Check-in is 24/7 with a self-service machine.