Since you are the Opera type I am just guessing that you might enjoy opulence and architecture. So that’s a lot of what I will recommend here.
You said you are flying in on 10/31? I hope not from the states. If you are and you are going to the Opera you are a better person than me. I would need a long, long nap before I could stay out that late. So Friday, if you have the energy make it a M1 Metro day. This is the oldest metro line on the continent of Europe. You will get on the metro in front of the Opera and take it to Vörösmarty tér (one end of the line). There you can walk a few yards to the river embankment for the view. Since you like the architecture then you might pop into the Gerbeaud Cukrászda for overpriced coffee and cake but excellent atmosphere and architecture and history. Then I would walk back to the Opera House only to get back on the M1 to almost the other end of the M1 Metro at Hero’s Square. Eat lunch at Paprika http://www.paprikavendeglo.hu/ Then I would take the metro back to the Opera House but stay on for a stop, then walk a stop and then back on for a stop and repeat. This way you get a bit of a view of Andrassy ut without having to walk the entire length.
get up, the K&K has a decent breakfast buffet, then walk to
St. Stephen's Basilica then
walk across the Chain Bridge to Buda, take the Funicular up and
visit Matthias Church and poke around Buda Hill for a while.
Now walk down to Batthyány tér where you can get on the
19/41 river front tram to Szent Gellért tér. See the hotel (research history)
Then cross the river on the Number 47/49 Tram and get off at the first stop at the other end.
You are at the Great Market. I “think” it will be open. Can’t swear to it. Ask them: http://budapestmarkethall.com/budapest-central-market-hall-opening-hours
Now take the Number 2 tram all the way down the embankment and around the Parliament building to its terminus. This is one of the world’s great tram rides.
At its terminus you will find the 4/6 Tram which you will take to the Wesselényi utca stop from which you will walk to the New York Palace Café (research the history). This is what the opera would look like if the opera were a coffee house.
Now take the 4/6 back to the Oktogon stop and walk to your hotel to get ready for the evening. Oh, did I suggest reservations at Menza for dinner after the concert/opera or what every decided on? http://www.menzaetterem.hu/menza_eng.php
LUNCH? Saturday during the tram tour if you get hungry just hop off. There is good food all over Budapest.
Hire a guide that will give you a world class tour of Jewish Budapest or what ever else interests you; after you see inside the Parliament. Then have the guide get you on your way to the airport.