Copenhagen Trip in November

Of the tree I would definitely go with Ribe. It's very atmospheric and fairly small. While I haven't been there in november, I doubt it will be total ghost town, people still live there year round.
Another option could be Helsingør. It is usually done as a day trip from Copenhagen, but no one says you can't spend a night or two there.
How do you plan on getting around? While you can certainly get to Ribe by public transport, a car will allow you to tour more of the surrounding area.

Transportation will depend on where we end up going I guess. Would love to do a train-only trip, but certainly willing to rent a car if needed. Thanks for the input.

Consider Odense. My wife and I spent two nights there in late September 2015. It has some good restaurants, enough to do (including some interesting museums and a beautiful park downtown), and a nice, extremely pedestrian-friendly downtown. And it is only about a 1.5 train ride from Copenhagen Central Station. We really enjoyed it.

I would not consider Odense a small town, it's the third largest city in Denmark (though that does not say a lot in a country with less than 6 mio people). I'm not personally a big fan of Odense, but it does have it's charms.
If you are really keen on going to Sweden, consider Lund instead of Malmø.

Fair point on Odense, but neither Aarhus nor Malmo are small towns either. And, at least for my limited time there, Odense felt like a smaller town to me and we really enjoyed it. Morten would know better than I would though, I spent 10 days in Denmark, he lives there!

None of these towns are seasonal. I.e. people live there all year round, go shopping, go dining.

I will cast another vote for Odense. We spent a long week-end there last year and enjoyed it. Ribe is another charming (and much smaller) town and there are many others, but Odense is the easiest one to reach from Copenhagen by public transport.

Actually not true. Roskilde is closer, but you can visit there as a day trip from Copenhagen.

Thanks so much for all the input! A couple of summers ago, we visited France and spent a week in Arles. If anyone is familiar with Arles, thats kind of the size/type of town we are shooting for - if that makes sense- or makes any difference in anyone's vote.

Larry mentioned in his OP that he didn't consider Aarhus or Malmø small towns and I would place Odense in that group as well, that's why I mentioned it Steve. Personally I have never been much impressed with Odense, but that's just my own personal opinion and I guess I have my biases as well (my last visit was for business fx.). It does not mean that other people can't enjoy it.
To put it in perspective here is a list of the cities and towns in Denmark by population https://en.wikipedia.org/wiki/List_of_cities_in_Denmark_by_population
Odense has a population of 176000, whereas Ribe only has 8000. However I think it is more important to consider if the historic center of the city or town is atmospheric, which Ribe has and Odenses also to some extent. Roskilde on the other hand has some world class sights (the cathedral and viking ship museum) but I don't think the historic center is that interesting, so it's not a place I would want to spend my evenings, but it's perfect for a day trip.
Helsingør which I recommended in my first post also has world class sights (Kronborg and the Maritime Museum) but a nice town centre as well, which I think is often overlooked by the day trippers.

I would say Aarhus is a bigger town but with a city filled of small-town feeling. I passed the city during a bike trip a couple of years ago and also went there in another mission 2016. I would recommend Aarhus but I would say this is the best season. Try visit the museum Aros in Aarhus, see http://www.bikedenmark.nu/aarhus/, the old town in central Aarhus. I also found it quite affordable to rent a hotel room here. You are able to get a bed for 25€ a night. Especially if you travel off season like November. Check it out here http://www.bikedenmark.nu/aarhus/lodging.html

I also agree with Morten about Helsingør. Lovely town with castles and museums to visit. It didn't suffer from the fires that Copenhagen had, so there are many old buildings. You can stop at Louisiana museum (a must do for anyone visiting Denmark) on the train trip there or back. Taking another train route back, you can see the palaces at Fredensborg and Hillerød. You could also tick off Sweden from there by taking the ferry across the narrow channel.

Our family members who live Copenhagen suggested that we visit Bornholm - it can be reached by bus or plane from Copenhagen. That’s where we are going for a couple of days in November. It looks fabulous.

Susan Bornholm is a lovely Island well worth a visit, though I would put it in the category of small towns as the OP requested. The Islands main town Rønne has some nice spots, but in my opinion it's not the most interesting place on the Island. That's the smaller fishing towns on the north coast, like Allinge, Gudhjem or Svaneke. And just the natural beauty of the Island and the massive castle ruins of Hammershus by the northern tip of the Island.