Heuriger with teens

Would regular tickets get us there?

Why not?

To make most efficient use of public transport, i.e. finding the best choice out of 20+ ticket variants, more information is needed.

I doubt that the trip to a Heurigen (wine drinking place) will be your only use of public transport. As you are 4 days in Vienna it is important to know what weekdays. The cheapest way to ride is using a week pass - even for just 4 days -, but it is a calendar week pass, i.e. valid from Monday 12am to next Monday 9am. E.g. for a stay from Saturday to Tuesday another solution would be better.

Your teens are too old for children's tickets. To qualify for a senior ticket (for single rides only) you must be older than 63 years.

By the way, your teens are old enough to enjoy wine at the Heurigen, given that the legal drinking age is 16 in Austria (18 for hard liquor).

We arrive in Vienna on Saturday. The weekly tickets are from Monday to Monday, I believe. We plan to go to the abbey at Melk on Monday. Our place is in Leopoldstadt close to the Taborstrasse station. I think we would enjoy walking to most of the places we want to visit.
We do want to do the ring road Rick Steves "tour," and we want to visit the gardens at Schonbrunn Palace. For these separated trips, I was thinking the 8 day sharable ticket would be good as you don't have to use it on consecutive days. The girls could use it for three trips with one extra. At that point we'd either buy another set of 10 or get individual tickets. They are one year too old for the 15 and under tickets, but young enough for the free museum entrances which will be a big savings.
They will be shocked to learn they could drink wine legally!

I think we would enjoy walking to most of the places we want to visit.

No way. Given the short time frame you have for Vienna, you should use public transport as often as possible. You will have several rides per day.

A senior's ride (using single ride tickets) is €1.50, a 72 hours ticket ist € €17.10, i.e. if you go 12 rides within 72 hours, which is not very much, you are already better off. For regular fare rides the break even point is at 7 rides.

I don't know at which time (and how) you will arrive and depart. If the time in between is maneageable with 72 hours tickets, it would be the cheapest option.

Agree. You won’t want to walk that much! Buy passes so you can just hop on a tram.

As for heurigen, please note that in the Spring this is really an afternoon event, not an evening event. You want to be in the garden in the sunshine!

I highly recommend Feuerwehr Wagner. I also highly recommend taking the 38a bus to Kahlenberg, enjoying the view and then walking down the hill following signposts for Stadtwanderweg 1. You’ll walk through vineyards and have amazing views of the Danube and the city. Stop at Mayer am Nussberg for a glass of wine and a nibble along the way. End with dinner at Feuerwehrwagner which isn’t far from the end of the Stadtwanderweg 1 or eat at Schuebel Auer, which is directly at the end of this walk. You can take Tram D back to the center. This is all within the city limits of Vienna so all passes for transport are valid.

https://www.mayeramnussberg.at/
https://www.schuebel-auer.at/
http://www.feuerwehrwagner.at/english/home.html
https://www.wien.gv.at/umwelt/wald/freizeit/wandern/wege/wanderweg1.html

Emily, thanks for those great ideas. We'll probably end up getting 3 day passes for all of us. My first trip to Vienna was in July, 1965 and I remember it being very warm. Memories: Frommer's Europe on $5 a Day, a 2 1/2 month Eurail pass (less than $200?), a packet of American Express checks, and fellow university friends who took advantage of the chartered prop jet which had to refuel in Gander. I had a hard time finding the Vienna hostel, as the address looked like a public square. Then someone pointed to an underground entrance where I found it. It seems like it was a converted bomb shelter with pod-like compartments. Can anyone give me a memory jog on that?
The pass was wonderful, even letting us do what's now called the fjord circle route. We finished the 3 month trip in England as it wasn't covered on the pass.
We were in Vienna in September, 2016, when there were many refugees being helped with food and aid. Travel continues to be a big part of my continuing education.

There is a tram that goes to Grirnzing. As I recall, it goes past Schubert's house, maybe where he was born or maybe where he lived.

Be sure to go toa place that has Schrammelmusik.