What to do in Italy for 7 to 14 days in November

Rome - Naples - Puglia sounds nice. Naples is not resort-y in the slightest. I would consider Sicily as well--depends on how quickly you like to move.
No weather guarantees in November, but I think it's a safe bet to stick south. Resort areas will be closing up for the season, so stick with cities and it should be grand.

The fact is that November and December are the wettest months of the year in much of southern Italy, on average.

The Wikipedia entries for most cities of tourist interest have climate-summary charts showing monthly average statistics. Content of the charts varies, but you'll nearly always find total rainfall, and sometimes you'll see the number of rainy days per month. Of course, there are temperature statistics as well. I don't find the Wikipedia charts sufficient in themselves to decide when I'm willing to travel somewhere, but you've already decided to go, so the question now is how you can maximize your experience. The charts are handy for comparing different options.

Although Naples averages a bit warmer than Rome in the fall, it is also wetter. Palermo's warmer than both the mainland cities. It typically gets more rain than Rome and less than Naples.

Siracusa, also in Sicily, is usually warmer and drier than Palermo. It's also drier than Rome.

Another area you might consider is Puglia. Lecce gets less rain than any of the other places I've mentioned. Daytime high temperatures fall between Rome and Palermo. Bari, also in Puglia, isn't quite as warm as Lecce but is even drier. I haven't been to Bari; it seems not as popular a destination as Lecce.

At a quick glance it seems there's more variation in average low temperatures than in average high temperatures. The Sicilian cities are a lot warmer at night than the other locations.

I am a bit concerned about “don’t particularly like Italian food” since that’s what is served in Italy, that’s one of the top reasons many people go to Italy and the Italians do it quite well. Perhaps versions of Italian you’ve had in the US are not authentic. Bigger cities have some other types of cuisine but there aren’t a wide variety of other types of foods and the “foreign” cuisines aren’t a focus.

Another worry I have about your post is Vienna is in Austria, not Italy. I’m unclear why you mention it here.

A lot of people start their first visits to Italy with Rome, Florence and Venice or a combination of those three. Since it will be Fall when you go, there are no guarantees that you’ll get good weather. You can check historical temps to see what it might be like.

We have enjoyed 2 previous trips in November to the Rome/Naples area. For us it was light jacket weather and we experienced very little rain. In Rome we ate Greek, Japanese and ‘poke’ meals in addition to Italian so I don’t think you will starve but you will have to source out alternatives. Naples is indeed ‘gritty’ and one of the most fascinating cities I have ever visited. Both cities are very walkable with great architecture. I would recommend both and Florence as well because each is different from the others in various ways.

Have edited my original post to clarify about the food situation. What I mean is, a lot of people would have food be one of the factors in the decision of where they go. Eg, I hear food in Naples is better than in Florence. But since I don't have it as a factor in my decision, I don't want food to influence people's answers. I don't plan on avoiding Italian food, but I'm also not going to focus on finding the best restaurants or anything. Just planning to eat whatever's available.

I have only been to Italy twice as an adult -- in 2003 and 2015 (plus once as a child). So, my depth of experience is limited. One comment I do have is that smaller cities that we visited (Orvieto, Lucca and Padova for example) have charms that the bigger cities may overwhelm. Still, Rome, Florence & Venice (and Naples?) have much in the way of history, art and churches (with their great frescoes and statues), while the smaller cities have less of that.

The good news is that you have enough time that you can mix it all up.

Have you considered Bologna? We’re here now and it’s still in the 80s (October) and I expect it will stay pretty nice for a while. Even if it’s rainy, there are miles of porticoes to keep you dry. Lots of museums, theater and places for tagliatelle with Ragu and apertivi. And it’s an energetic city because if all the college students.

Another positive for Bologna is its transportation system — you can take a high-speed train from Bologna to any number of places, including Naples.