Sunday mid-afternoon arrive Budapest
When I arrive after a long flight I find if I take a shower and put on clean clothes and then get out and remain active until a normal bed time I do pretty good that day and much better the rest of the trip.
So, I would do that and head straight for the Vorosmarty ter markets. For you that will mean the short walk to the Oktogon and getting on the M1 metro. Yes, skip the Andrassy ut walk for the first day.
After walking the Vorosmarty ter markets I would walk to the river its only a few hundred meters away. The lights are stunning at night.
You are tired but you still have to eat, so make reservations at https://www.dunacorso.hu/ to have a really Hungarian experience.
Now you choose. The M1 home or walk up Andrassy ut. If you are up to it the lights in the winter are beautiful. If not, then there will be other nights, and take the metro home.
Monday Budapest
Metropolitan Ervin Szabó Library? You have class. Sounds like a 47/49 tram day. Walk to the end of Andrassy ut and board the Tram at Deak Ferenc ter. First stop is the Dohany utca Synagogue (Great Synagogue), second stop is Metropolitan Ervin Szabó Library, third stop is the Great Market Hall.
Then the 2 tram to the Parliament and there are some places there for a late lunch. Do the shoes maybe then walk down Falk Miska utca to a place called Pinter https://pinteraukcioshaz.hu/ I think you will enjoy the art and the antiques in the basement. Actually the street is lined with similar smaller shops of art and antiques.
Falk Miska utca ends at the 4/6 tram line which will take you back to Oktogon and your hotel. Sit on the left and see the Comedy Theater and the Nyugati Train Station and just a lot of great old Hungarian architecture.
Tuesday Budapest
Okay, Andrassy ut day.
Do the House of Terror in the morning. Its actually very well done. Then walk to the bath house. Long walk but past some great architecture. The lower end of Andrassy ut is high end shops, the mid portion is these amazing old massive apartment blocks and the upper end is mostly mansions and embassies. Then Heroes’ Square then the park and the bath house. If you get tired the M1 runs under Andrassy ut and has a station at the bath house.
After your bath you have to see the Hungarian House of Music. Maybe have lunch at https://paprikavendeglo.hu/ then head down Városligeti fasor, the original Andrassy ut, where the architecture will blow you away. And where ResoArt, which you have to see. Figure it out and I will go with you. Don’t miss it; and where the https://www.imm.hu/hu/contents/262,R%C3%A1th+Gy%C3%B6rgy-villa is located which I enjoyed a lot (I am an architect, which explains the interest in both).
Given my guess of what interest you, sometimes the Opus Jazz Club has concert/dinners on Tuesday. I would to that before a church concert. If you do the church concert then we find you a really special last night dinner.
Wednesday after lunch train to Vienna
After lunch because there is at least once place you wanted to go back to or at least once place you didn’t yet reach. The train tickets are cheap, and if you change your mind about departure time, it’s a 60 euro penalty (new tickets) for two.