Booked six nights this December

Pension Suzanne was wonderful when I stayed there in 2018. Very friendly team and (back then) a nice breakfast spread. The location - near the opera house - is superb. I enjoyed seeing the opera house by way of a ballet, rather than a tour. Perhaps they perform The Nutcracker; the December schedule isn't available to check.

I had a very nice WienerSchnitzel meal, outdoors at the Naschmarket.

I will join CWSocial in praising Pension Suzanne. I stayed there in March 2015. Super friendly owners and great breakfasts. I went where the owners recommended for a Schnitzel. It was good, but I don’t remember where it was.

We had a fabulous schnitzel at the Palmenhaus restaurant which is a former Royal greenhouse. Besides the great meal, the setting was beautiful. Just a tip, if you want to save a few dollars on your meals in Vienna, have a late lunch/early dinner. During lunch they usually do not use formal table linens, usually paper napkins and placemats. Most restaurants add a fee for the table linens. We discovered this our first night in Vienna. When our bill came we asked what the extra charge was, thinking they may have added a tip. But the waitress told us it was a service charge for the linens. The difference in cost between lunch and dinner we found to be substantial. We usually don’t fret over price but don’t spend needlessly either.

"Where do you get the best Schnitzel in Vienna?"

This is a highly contested question, even among locals. You are opening a can of worms here.

First you have to decide which of the three classic variants you want. (I am leaving out the more unconventional stuff, though sometimes good, too.)
1. Wiener Schnitzel made from veal - the original
2. Schweinsschnitzel made from pork - the most consumed (>90%)
3. Surschnitzel made from cured pork - the juicy and most tender one (my personal favorite)

These are the places I can recommend for the respective variant (the numbers refer to the city boroughs):
1. Meierei Stadtpark (3rd)
2. Schnitzelwirt (7th)
3. Heuriger 10er Marie (16th)

I am unfamiliar with the linen fee that Barbara describes and I've eaten at the Palmenhaus many, many times. That said, most restaurants offer a 2-3 course lunch menu, which is fixed, for a very good price - even the more expensive restaurants.

As for good schnitzel, I'll offer my favorites:

1. Gasthaus Pöschl (1st) and also the best atmosphere anywhere
2. Concordia-Schlössl (10th) right next to the main cemetery (Zentralfriedhof)
3. Café Rüdigerhof (5th) in a fantastic art nouveau building
4. Figlmueller (1st) or its sister Lugeck, they are famous for a good reason

I visit Vienna at least once a year and can second Emily's recommendation for Figlmüller or Lugeck. Definitely make a reservation - easy to do online and saves a lot of hassle. Usually easier to get a table at the Bäckerstrasse location and helps if you don't mind eating on the earlier side.
Figlmüller is very popular with tourists and is on the higher end price-wise, but in this case, it's one of those places that is actually good. I visit Vienna at least once a year and always eat at one or both of Figlmüller/Lugeck - never been disappointed!

Just wanted to chime in about schnitzel: my husband and I visited in December 2019 and our meal at Figlmüller Wollzeile was a highlight of our trip. We asked our hotel to make lunch reservations and we had the best experience. Excellent schnitzel, lovely atmosphere and very good service. People without reservations were being turned away left and right. I'd go again in a heartbeat.

Schnitzelwirt, near the K&T boarding house -- I don't remember whether they had table linens but I do remember huge schnitzel (on subsequent visits we ordered ONE schnitzel with two potato salads for the two of us.) Seemed to be mostly locals -- maybe "regulars" -- but the staff was welcoming to non-locals.
Hoping to be able to get to Vienna for New Year's Eve.

I will attempt to try them all. I do so hope that the situation allows the borders to open. The world needs the joy a Christmas market brings. (I know that I do!)