what's open after Nov.1 ?

Where is Italy are you questioning?

Rome, Florence, Venice are not the same category as Vernazza & Positano etc.

For specific attractions (museums, etc.) it's best to check their website for closures.

You need to be more specific
What do you mean by “touristy areas” ?

Of course “Italy” isn’t closed after Nov 1

All major tourist sites/cities/towns will certainly be open year round

Some businesses in small tourist towns might be closed

As above, where are you intending on going? It makes a big difference. "Touristy" is a fuzzy term: Rome draws tons of of visitors and is open for business all year. Capri, on the other hand, is very busy during the warmer months but goes quiet in winter.

Sorry didn’t phrase question very well. We’re going to Rome, driving to Trani, Polignano a Mare, Alberobello, Locorotondo, Martina Franca, Ostuni, Lecce and back to Rome. The part on the Adriatic would be first week of November. Thank you!

I wouldn’t consider any of those towns as strictly “touristy”

I wouldn't be surprised if some activities are unavailable that late in the season--things like the walking tour of Lecce I enjoyed in 2015. It's possible some sights (churches or minor museums) might have more limited opening hours in November, maybe even weekends only in some cases.

Is it sightseeing attractions you're worried about, or is it shops and/or restaurants?

You could do an experiment on booking.com: Check availability of a double hotel room for one night during the first week of September in, say, Polignano a Mare. How many lodging places does booking.com find? Now check for the same day of the week in early November. Is the number of lodgings a lot lower?

There will be some restaurants closed because the people who run them like to have a break after October and before Christmas, and since November 1 and 2 are All Saints' Day and All Souls' Day, it's a good time to start the break. The towns that are mostly beach towns do shut down in winter and will look pretty bleak. There aren't a lot of museums in Puglia --- the only one that springs to mind is the transportation museum in Lecce. There should be plenty of cooking classes, tours, etc in Lecce.

Shops and even churches in Puglia year-round will be closed all afternoon, but restaurants are open for lunch so we usually eat a long leisurely lunch then and go look at the exteriors of the Romanesque churches (often the only part I want to see anyway) or ramble around the semi-deserted town or drive somewhere or take a nap. But towns are lively and open in the evening. Lots of people strolling around before dinner. For instance, the outdoor fish market in Trani is open at night, as are places like butcher shops and wine stores that would be closed earlier in the US. I would be amazed if a single business in Alberobello is closed.

We've spent several weeks total in Puglia in November and think it's a great time to be there. Olive harvest, farmers markets, great weather, no beach scene, and wonderful food including for the holiday, a traditional dish of colva (cooked wheat grains, pomegranate seeds, nuts, vincotto, and chocolate).

That’s very helpful, thank you. Do you know if gas stations will be open November 1, that's the day would drive from Rome to Trani.

Ginny, locals need to gas their vehicles too. This might be helpful, although I'd love for one of our experienced drivers to check it for accuracy:

https://mominitaly.com/italian-gas-stations/

Although some businesses (like B&B) may close in winter at some small locations, while others may observe shorter opening hours, however local Italians do not go into hibernation in winter like bears. The places you mentioned, even the smaller towns, do have local residents year around. They have to eat and shop too.

Thank you. I’m a worrier, afraid everyone hibernates.

Kathy - Do you have a restaurant rec for Lecce and/or Trani? Also, how do I find out about olive festivals? That sounds fun. The link you sent about gas stations helps too. Thanks.

That’s very helpful, thank you. Do you know if gas stations will be open November 1, that's the day would drive from Rome to Trani.

Gas stations on A-something Freeways are always open. Same on local roads, but you'll have to use the self-service fuel pumps almost everywhere. In case of problems with your credit card, keep in reserve two € 20s.

Kathy - Do you have a restaurant rec for Lecce and/or Trani?

Sorry, afraid I'm no help in that area.

We went to Tuscany two weeks before Christmas. Museums, cathedrals, restaurants, etc. were all open. Although the days were short, it was a great time to be there. There were no crowds, except the last Saturday before Christmas in Rome. All the citizens were out shopping.