First leg of a 2021 trip: Vienna

Actually you can do more on one day than you indicate. We went to the Naturhistorisches Museum - it has the famous Venus figure (oldest object I have ever seen). I'd say we spent 3 hours there. You could do that in the morning, have a lunch, and then go to the Belvedere history.

To get to the Heurigen, we took the bus. They were lots of fun - very pleasant - depending on the time of year, of course.

I'd plan time as well at the Schonbrun Palace. I've been there 3 times, and never been inside. The gardens are quite nice, and worth a trip.

RS walking tour is very helpful. There are also churches in the historical center. Some have daily music.

When we were there almost 9 years ago, the "Mozart men" were all over, trying to get you to pay for an overpriced concert of "war horses". I'm sure the music is good, since the orchestra has played the same thing for 20 years. Also watch for gypsies selling flowers and stuff. Annoying but they go away if you ignore them.

I would plan to eat at the Kunsthistorisches Museum restaurant while you're there. The setting is gorgeous.

Regarding the Natural History Museum... have you been to the one in Washington? Or even the Field Museum in Chicago? Vienna’s feels very similar. Lots of large models of animals. Lots of fossils and rocks and the like. Much more kid geared in feeling overall.

We went for 20 minutes to use the restroom and see the Venus of Willendorf (had the Vienna Pass), which was the only thing I wanted to see. Natural History Museums are just not my cup of tea but it’s a great museum if it is.

Now the Kunsthistorisches on the other hand... I could have spent hours more than we did. And we spent 4 hours there.

I have quite a few thoughts.

Day 1 - Do the Schonbrunn instead of the Hofburg. The Schonbrunn is a fantastic combo of indoor and outdoor. The Hofburg is really not that interesting outside or inside, in my opinion (unless you are a big Sisi fan). The Volksgarten is a lovely public garden known for its roses. Really can be explored in about 20-30 minutes (and I love roses). No one calls the first district the "Old Town."
Day 2 - The Natural History Museum. I've probably been there 20-25 times. I can't stand it, but I go there because my kids loved it from the ages of 3-6. It is full of old, dead, stuffed animals, primarily and rooms and rooms of rocks. The best part is the Venus of Willendorf, but, honestly, you can see that in about 5 minutes. So many better choices of museums, including the Military History Museum, the Technical Museum by the Schonbrunn and the Welt Museum.
Day 3 - It is a palace not a castle. The Belvedere is a solid choice and my favorite art museum in Vienna as the setting is just as beautiful as the art. The Naschmarkt is nowhere near the Belvedere, not quite sure where you got that idea. I actually can't stand the Naschmarkt as it is now full of junky tourist shops selling tat rather than authentic stalls.

Day 4 - All you are doing is visiting a heuriger? That is a late afternoon thing. What else are you doing that day? Grinzing is terrible, in my opinion.
Day 5 - KHM. Fair choice and top tier art. Building is beautiful
Day 6 - Twin City Liner - please don't. Waste of time and money.

Here's what I would do instead:

Arrival day - do a self-guided walking tour of the first district, which would include the Volksgarten and the exterior of the Hofburg as well as a stop at the Cafe Landtmann for strudel and coffee.
Day 1 - Schonbrunn, inside and outside
Day 2 - Belvedere and the Military History Museum (with a stop for lunch in between at Klein Steiermark)
Day 3 - KHM during the morning. After lunch, take the 38A bus to Kahlenberg and walk down the hill stopping at Sirbu or Mayer am Nussberg on the way down for wine/grape juice and nibbles. End at Schuebel-Auer heuriger.
Day 4 (or whatever day is a Saturday) - Visit either Karmelitermarkt or Brunnenmarkt for a great market experience, but go in the morning. In the afternoon, I suggest the Albertina. Have a sausage from the Bitzinger Sausage stand just outside of the Albertina (it has a pink bunny on top) for lunch). Have cake and coffee at Diglas and dinner at Fliglmuller.
Day 5 - Go to the Alte Donau, rent boats and explore this old arm of the Danube checking out the cute river houses. Take the train in the evening to Bratislava (45 minute ride).

We probably spent about 2.5-3 hrs in the Natural History museum - the first dozen or so rooms we just sped thru - rooms full of cases of rocks (I NEVER want to see another piece of rock - ugh) and other stuff that I've 'been there, seen that'. The rooms after were much more interesting (IMO), but I still vowed to never go to another NH museum (I've been to so many).

Don't forget Karlskirche and when you're exploring around St Stephen's - do yourself a favour and visit the Jesuitenkirche - I loved it - so over the top.

Naschmarkt was OK for us - we didn't buy anything (oh - I lie - we did pop into a store selling chocolate and Manner wafer cookies - I'm sure that was at the Nasch and we did pick up some cookies), and it seemed like a lot of repetitive stuff and people trying to get you to take food samples (whether you wanted to or not) - the dried food/spice area was interesting. And we went on the morning they have a flea market, but (in my eyes) it was mostly junk and didn't see anything that I wouldn't find at home.

Thanks everyone for all the information. I clearly need to do some more studying—but I have lots of time and you have given me some good direction. Emily, I particularly appreciate your local perspective and will definitely follow up on your suggestions. My thought with the Hofburg and Volksgarten on the first full day was that we will be jet-lagged (I do not recover quickly) and may just want to sit in the garden; then we could tour the Hofburg if we want, or just look at it if we don’t, but I guess that could apply to Schonbrunn just as well. When comparing the Hofburg to Schonbrunn, does one have more of a historical vs. “lovely royal rooms” emphasis to the toured areas? Regarding the natural history museum, I am a former biologist, so I do like to visit science-oriented places, which are not typically emphasized in guidebooks. I loved the Gallery of Paleontology and Comparative Anatomy at the Jardin des Plantes in Paris, for example. But the responses here suggest that the museum in Vienna is rather old-style, so at least we probably don’t need to allot a lot of time there; we do need to see the Venus of Willendorf—and at least one rock, if it’s on display. Last year we toured an opal mine in Slovakia, and in the Vienna museum they have the largest opal ever taken from there.

But the responses here suggest that the museum in Vienna is rather old-style,

This is not the case, except that the NHM's building is more than 130 years old. Especially the temporary exhibitions are outstanding.
E.g., the museum has the world's largest collection of meteorites. In the gemstone hall various precious stones, gold and platinum nuggets are on display, and most notably the bouquet of flowers made from more than 2000 diamonds and 700 other gems, which empress Maria Theresia (whose monument is in front of the museum) presented to her husband as morning gift after their wedding night.

https://www.nhm-wien.ac.at/en

Thank you wmt1. I can't believe I had previously missed so much of the information on that website. So embarrassing. I am sure we would be able to spend quite some time with the fossils (dinos! fossil snake!) and the anthropology exhibits (bronze age sculpture!), and even a few more of the "rocks" (the biggest opal! meteorites! gemstone bouquet!). I think a half a day for sure.

There are so many sites central to the Ring. The Opera is stunning, and those that mentioned St. Stephens are correct - it is a must. Belvedere is fantastic, and any opportunity to sample a Kasekrainer is a must! The Habsburg burial crypt is also a fascinating stop while you are in the Ring. And what would a trip be without a Sachertort? Have a great time. I spent a semester there in college and returned for my honeymoon and will go back again when opportunity is there.