If I answer here maybe someone else gets use out of it.
DATES Your dates are pretty prime for being here for the Christmas holidays. The markets are up and going strong and strong but the heaviest influx of tourists hasn’t yet arrived.
GYÖR: The idea of spending a night in Győr on the way down from Vienna is also top notch. The market is very nice: https://youtube.com/shorts/TCzQmOWj9fg?si=N4tqg7o9QeNTxJr5 Last year it opened on 28 December. This year the corresponding date would be 27 November. If you don’t have reservations in Győr yet, I like the Hotel Klastrom. It’s a nice 3-star hotel with good reviews (besides my own) and a great location. But most fun is that it is a converted 18th century cloister. https://klastrom.hu/.
PANNONHALMA: Do spend time at the Pannonhalma Archabbery while you are in Győr. There is a bus you can take from Győr, but a taxi is probably easier. TexasTravelMom maybe will chime in on the bus information. One goes closer I think and I think one has a bit of a chilly walk. Here is their website https://turizmus.pannonhalmifoapatsag.hu/ . It’s a bit early but watch their website for concerts, you might get lucky with their dates.
SZENTENDRE: A great day trip. But you are spending enough time in Budapest where you might want to make it at least an into the evening trip so you can see the Christmas Market after sunset (that will be about 4pm and truly dark by 4:30pm. Then the world comes alive with lights. https://youtube.com/shorts/XjloLPd8qWE?si=tFSU3yMw_yJQFzkK The early sunset works for the beauty of the region. Its winter so no boat back to Budapest from Szentendre, but the commuter train is good. Here is a not very good trip report on reaching Szentendre: https://community.ricksteves.com/travel-forum/hungary/trip-report-day-1-833-szentendre-day-trip
BUDAPEST: You have my list of hotels (at Christmas you can’t beat Andrassy ut because of the lights and atmosphere) and restaurants (make reservations at least a day early) and things to do in the winter in Budapest and there are a lot of good posts on the subject too. Buying train tickets on the app when you are not in Europe continues to be an issue, but you should have no trouble buying them online with a computer. But its way early for that. If you are over 65 then the Győr to Budapest ticket is free except for the seat assignment (about 2 euro).
Winter is theater season, buy early for the best seats. If you want a more Hungarian experience go to the Opera or Operett on a Friday or Saturday evening and get the best seats you can afford (by world standards they are cheap) … weekdays and cheap seats tend to be mostly tourists. Then if you want to kick it up a notch from there, go to a playhouse. A few in town do plays in English or with English subtitles. I mean does it matter to see CATS in English or Hungarian? (but it has English subtitles). But there will be nearly 100% locals in attendance. Some of the playhouses are truly beautiful venues as well. https://lelepo.hu/wp-content/uploads/2023/09/vigszinhaz3.jpg
A hint for any performance with subtitles, sit high, sit in a box. Makes it easier to see the subtitles (actually surtitles projected above the proscenium opening).
The Christmas Markets here are very well done. Here is my poop on the subject: https://community.ricksteves.com/travel-forum/hungary/budapest-christmas-markets-d26f8ab1-2048-4160-bfb3-bf13b096683e For your visit to Vienna, Emily has taken the time to detail all of the markets there. Look for her post. Excellent.
Remind me a little closer to the dates and I will look for an art showing to attend. We might get lucky.
Also keep an eye on https://community.ricksteves.com/travel-forum/hungary/updated-budapest-events-for-january-june-2026 I will update November and December and add more as dates are set.