Perche

I lived in Seattle for 12 years. Because of the dampness, 45 degrees in Seattle felt colder than 15 degrees in Boston. Venice is similar. In January or February you are cold, no matter what. That said, if you haven't been to Venice, consider just going there and renting an apartment. You can actually live like a Venetian at that time of the year. It may be the prettiest city in the world. it also climbs over almost all of the competition as the most romantic winter city in the world.

There is no better way to experience Italy after you've buzzed through the tourism hot spots than to go there, rent an apartment, and live like a local. There is no better place to do that than Venice in January because the tourist-free window that allows you to see the city in all of its splendor is very short.

You can rent a nice apartment there in the Castello district. Get up, have coffee, go to the market, take an Italian-language/cooking/wine-tasting/rowing class, or just walk around.

Since you've been there and done a lot of the tourist places, another option to consider is to just go way down south, where the weather is still nice. Southern Italy has the best food, beaches, ruins, scenery, and everything else that is good about Italy. Italy just hasn't invested in it, so tourists don't routinely go there.

With ten days to spend unless you are really fixed on staying in the North, you could go to Naples, or even to Sicily. You can take a train from Genoa/Rome/Naples all the way to Palermo, Sicily. It's an overnighter, a train with a sleeper bed and a private bathroom, like in the movies. It costs less than a hotel. The train drives right onto a ferry and crosses the sea to Sicily. You can stay on the train all the way to Palermo, where you won't even need a coat, just a light sweater at night. From Palermo if you rent a car or take a train or bus there is almost no end of Greek and Roman ruins, and small towns that you can see. Arrive in Milan in the morning, be in Sicily the next morning, no driving, and you'll never eat better.

When you are done you can take a ferry boat from Palermo all the way to Genoa. It's a nice boat with private sleeper cabins and no train, that is also very cheap compared to a hotel. From Genoa back to Milan is a short, 90 minute train ride.

You have a lot of options. Winter being what it is, I don't think that hitting a bunch of towns would be very fulfilling. Maybe stay in Venice and get to know the place, with a day trip to Trieste, Verona, or even Bolzano, which for all intents and purposes, is Austria, except for a WW 2-related moving of the border that didn't affect the culture, language, or food. The Alto-Adige region is more German than Italian. Basing yourself in Venice during the winter without the tourists, you can do both, as if visiting two countries. The people in Alto-Adige won't even call it that. They insist on calling it Sud-Tirol, or the southern part of the Tyrollean mountains, as if they are still in Germany. Go pick up a nice bottle of white wine from there and you'll see what I mean: it will say Alto-Adige, Sud-Tirol. You can do that during a ten day trip to Venice. You can ski, or even bobsled in the Sud-Tirol if you want.

A boat to Palermo with nice, warm weather and side trips to visit more ancient Greek and Roman ruins than you can find, or Venice, Verona, and Alto Adige-wow! Since you are going in January you have a lot of options that tourists normally don't have.