Vienna in 3 days during Christmas Markets

Lodging (not necessarily fancy but maybe atmospheric and easy to airport)?

As you arrive by train from Budapest at Vienna's main train station, also where from the express trains to the airport depart, it would make sense to stay in one of the new modern hotels right at the train station.

I am confused by the dates on the schedule notes.
11/30 (Sun) the last day of November is a Monday. You will arrive in Budapest on the boat?
12/1 (Tues) Then the next morning after arriving in Budapest you take the train to Vienna?
12/2 Vienna
12/3 Depart

You want to spend time in Vienna “Old Town”, which I guess you mean within the Ringstrasse, so that’s where you should stay, “within the Ringstrasse”. With so little time I think it makes the best sense. Within or on just outside on the southern side.

For lodging in Vienna, I plugged your dates into booking.com to see what is available at a decent rate. Easy to the airport is not a thing at the moment as nearly all of the train service is interrupted and running with replacement buses until October 2027. That said, you can take the Railjet train from the airport to Hauptbahnhof, which is on the U1 subway line, which will get you anywhere. For me, I would recommend spending another 10 minutes on public transportation to get you to a nicer part of town instead of the soulless area around the Hauptbahnhof (main train station).

My suggestions:

1. Boutiquehotel Das Tyrol - on the main shopping street, very nice hotel, decent price for December, very near to some of the best markets.

2. Hotel Motto - Another winner at a decent rate on Mariahilferstrasse (the main shopping street). The Motto Bakery on the ground floor is excellent.

3. Hotel Indigo at Naschmarkt - Again, a winning location near the Naschmarkt and not far from Christmas markets. Modern design, but very good quality. My business guests always stay here. The neighborhood is very good - check out Silberwirt and Zum Alten Fassl for dinner.

4. Singerstrasse 21-25 Aparthotel - Very good price for probably the best location in the entire city. I stayed here when I moved to Vienna for a month and liked my stay.

5. Boutique Hotel Spiess & Spiess - Tucked in a quiet street (near my apartment) but right next to a subway stop, this might be the ultimate hotel secret in Vienna. An absolute turn of the century stunner, this hotel is amazing value. I think this would be my favorite in this list.

6. Buxbaum Beletage Design & Boutique Hotel - This is a new hotel which grew as an offshoot of a really nice restaurant. The price includes breakfast and the location is right in the middle of things.

7. Hotel Gilbert - Ok, this one. Right at the best Christmas Market in the city (Spittelberg) and just behind a few others. For Christmas Markets, this is the best location. Known for very good breakfasts as well.

I am going to stop my list there but if these do not suit your budget, I can look again.

When you dock in Vienna on your cruise, maybe you want to spend that day visiting Schonbrunn so that you can spend your longer stay in areas closer to the city center?

As Mr. E points out, there is no "old town" in Vienna as most everything here was demolished either by Franz Joseph or by WW2 bombs. What exists now mainly dates from the 1880s to present, but you can find older gems if you know where to look (the Cathedral is the obvious one, but it was rebuilt after the war). You are likely referring to the First District (Innerestadt) which is inside of the Ringstrasse.

What excursions do you plan to do with Viking on December 1st? The included excursion looks to be an interesting intro to Vienna. Then, you can do either Schönbrunn or Belvedere, for example. I expect that these excursions will focus on the museums themselves and you won't have any time to visit their respective Christmas Markets.