Suggestions on Our 2 Week October Itenerary to Hungary

Sounds like a glorious adventure

My friend and will be in Hungary from Oct 9-24. We both enjoy history
(for me especially the communist era),

Then you want to see the Hospital in the Rock and go to the Retro Museum. Maybe do a tour in Lada or a Trabant or a UAZ.

architecture,

I will send you a link that includes a sort of off the beaten path road for architecture. Otherwise an architecture related tour might be the ticket. Google, there are several.

culture, and wine.

I will send you a list of wine bars

We plan to visit a thermal bath most days if possible.

The three I would try and make, just because each is unique, would be Gellert, Széchenyi and Lukacs

While in Budapest our must sees are Parliament, Memento Park, House of
Terror, the great synagogue, the children's railway, Vajdahunyad
Castle, and all the other walkable sights.

Memento Park and the Children’s Railroad are not exactly walkable. But worth the effort.
Since you mentioned architecture before when you go to Vajdahunyad and Szechenyi look for the Hungarian House of Music and the new Museum of Etnography in the Park.

We're planning take a day trip to Szentendre (including the Open Air
Folk Museum).

Unfortunately the boat stops running in mid-September. But in past years they have extended a few weeks if the weather was good, and they thought they would have the customers. So check when you get here. But the train is fast and efficient and free for old farts like me.

Cant help much with the National Parks. Sorry.

Thank you, Mr E for taking time out to comment on my itinerary. Just out of curiosity, is there a benefit of going to the Lukacs over the Rudas baths. My brain is filled with so much research I can't remember why we picked Rudas (the other two were on out list). In the end we're happy to try anything a local would recommend.

Rudas is great. I only suggested Lukacs because it's more of a local hang out .... just for the change.

If I were in the mood for nature, I would leave all but a carryon in my Budapest Airbnb then hop Wizz Air to Podgorica and go up into the high country for a few days. Few places as beautiful. As little as $100 rt in about an hour.

I have not been to Lukacs yet, but agree it is probably just a matter of choice.

Thank you. We may just try out Lukacs because Mr E (wherever he is) suggested it as more local.

They are all good, all different and all life experiences. You just cant do wrong, no matter what you choose.