Itinerary Help / Critique

Day 1: October 20th (Sunday) (is this too aggressive for one day?)

Buda castle hill Fisherman’s Bastion Buda castle museum(s) Matthias
Church Hospital in the rock Labyrinth Citadella

Depending on where you are staying, etc. Its a full day, but not a bad day. You still need an evening activity.

Day 2 and 3 activities I'd like help organizing by day:

Széchenyi Baths Shoes on the Danube St. Stephen's basilica Hero's
square Vajdahunyad Hungarian railway museum Opera house House of
terror Great synagogue Hungarian national museum Great market hall
Holocaust memorial center National history Museum Parliament

Okay I would do Andrassy ut one day, everything else the next.
So

Day 2 Assuming you are staying near the lower end of Andrassy ut.. Here the M1 metro line can supplement the walking a bit. You will need a bus to get to the railway museum. I think its worth the effort. The bus stop is near Hero's square.

House of Terror (do first to avoid lines)
Vajdahunyad
Heros's Square
Railway Museum
Széchenyi Baths
Opera house ( i believe there are tours around 5 pm, so head back there on the M1 for the tour, then go to the baths if thats how the timing works out).

Day 3 Assuming you are staying near the lower end of Andrassy ut.
This day uses the 47/49 tram and the 2 tram for most of the getting around. The holocaust memorial center will require a short trip on the M3 metro at Kalvin ter. And you need an evening activity.

Great synagogue
Hungarian national museum
Holocaust memorial center
Great market hall
Parliament
Shoes on the Danube
Basilica

Thanks James! Very helpful. I think though on day 2 (Monday), both the House of Terror and the Railway museum would be closed.

If I simply switched the day 1 and 2 itineraries, would that solve that issue?

You are correct. That's why with out dates and hotel locations this is impossible. Didnt notice the dates in your post the first time I read it. I think the Train Museum might be closed on Monday too. Best double check.