The State Opera House offers the best classical concerts in town. Standing tickets start at 300 ft (about 1.50$) while the cheapest seat, that still offers a really good view, costs 800 ft (about 4.00$). This is by far the best price you can find for a high quality opera in Europe.
The building itself is worth a visit. I bought the cheapest seat, which gave me a good view at the beautifully painted ceiling.
If possible, leave the jeans and t-shirt in the suitcase and put on the nicest suit you brought. If you don't have anything other than jeans and t-shirt, be prepared to be looked at as a disgusting alien and sent to the side door to the balcony (I speak by experience).
I had the chance to listen to a Hungarian opera, by Kodaly. There is no translation, but the program (costs 250ft, about 1.25$) provides a short resume of the plot in English. The second part was a ballet, also by a Hungarian composer. Both performances were of very high quality and could satisfy connoisseurs.
If you are afraid of Hungarian unknown operas, know that more famous operas are also performed. The previous night had Mozart's La Nozze di Figaro on its programm.