If possible, try to get tickets to the Opera house for one night that you're there. It's the best sounding opera house in Europe after the Scala in Milan. If the place looks familiar, it's probably because you've seen it in a dozen or so hollywood movies as a movie location. If you get tickets (they tend to be reasonable), make sure to dress up :)
From the opera house, keep walking down '''Andrassy''' street (''ut.'' stands for ''utica'', hungarian for ''street''), about 5 blocks, and look to the right. You'll see '''St. Stephens''' basilica when you come up to a larger square. The church is named after the founder of Hungary. For the way back, you can use the subway M1 that runs along '''Andrassy''' street for two stations, back to '''Octogon''''. While riding the M1 metro line, look at the design of the metro stations. This metro line is the oldest subway on mainland Europe.
==== Parliament building ====