Which additional city would you add to this northern Italy itinerary?

Padua is one. And Siena if going to Tuscany.

You don't say how long you have for the extra city, but plotting your route on a map and imagining you don't want to return somewhere you've already been for the extra city, I'd suggest either, for a shorter stay - one night:
Novara (very pleasant and very untouristy) - we spent part of a day there but could easily have stayed longer. This is my visit: https://slowtravelitalyspain.blogspot.com/2023/07/novara.html
Or for a couple of nights or more something totally different from the other northern Italy cities
Genova - a bit chaotic with the cavalcavia by the port but I loved it - Boccadasse - on foot or by bus from the centre, is very pretty and the Unesco site Strade Nuove Palazzi dei Rolli, etc etc, lots to see and not on the usual tourist beaten track

If I consider Tuscany or nearby, I have stayed at Lucca, Siena, Montepulciano & Arezzo. Arezzo’s jousting festival will be happening while I am in Italy. It was fun to attend it back in 2022.

Thank you for the reply, Kenko! Padua is another spelling for Padova. My husband & I stayed there for five nights in 2007 and enjoyed it.

Tinac, Novara & nearby Vercelli could be a nice choice - thank you!

Treviso, Bassano del grappa, the cities of Friuli-Venezia Giulia

I enjoyed Brescia although it is seldom mentioned as place to visit but it fits in exactly with your route. Amazing Roman ruins, Unesco site, series of great interconnecting piazzas with varying degrees of public art and a castle on top of hill to round things out.

Trento is (sort of) in the area and also on my list, but I haven't had a chance to get there yet.

Sounds like a great trip!
=Tod

I haven’t been there, but I am intrigued by the idea of Asolo.

If going to Tuscany, Lucca is a must. We are their now. We also had a couple of lovely days at Genoa and for a short drive further along the coast in Monaco.

Except for the horrible heat, I enjoyed Udine, Treviso, Brescia and Trento this August. September could be a lot better, weather-wise, especially if you're not there at the very beginning of the month. I'd say none of those have the sort of high-level sights available in places like Ravenna and Padova, but they're very pleasant for a day or two if you get decent weather for strolling. If it's as hot for you as it was for me, you may be the only person outdoors for much of the day.

There's a good modern-art museum in Rovereto, an easy day trip from Trento.

I got bitten by mosquitos or some smaller insects around dusk in both Udine and Treviso. That's a rare event for me.

Tobia, thank you! I haven’t spent any days in the Friuli-Venezia Giulia region, yet.

Tod, thank you for mentioning Brescia. It sounds like it has it all! : )

My husband & I spent an afternoon & night at Trento on the way back from Moena. For Trento, we stayed at the Hotel Villa Madruzzo which still gets great reviews. There’s the lovely grand villa, plus a modern building near it; the photos will be apparent which rooms are in the villa. We had a fantastic dinner there!

Our usual mode was public transportation unless we really needed a taxi. I had the bus number to take from the train station, and over & up the hill we went. Partway up, the bus had a problem, and we all had to get off. We followed the others, walking up the hill - us with roller bags. A few minutes later, the bus started, and he came up and picked us allup again to proceed. I knew a rough idea of where to get off, but not really anything specific- back in the less-technology days. So, I politely asked a person on the bus, and so many riders suddenly wanted to help, too! When our stop came, several told us and pointed which way to walk to eventually arrive. : ). We did take a taxi the next morning back to the train station. ; )

If you decide to do Brescia I'd recommend taking the metro one stop from the train station to Vittoria to avoid walking through the "everyday Italy" that exists between the train station and the old core. It's fine but it's certainly not very interesting. Starting at chain together Piazza Mercato to Piazza della Vittoria to Piazza della Loggia to Piazza della Loggia to Piazza Paolo IV with the old and new churches.

The Roman ruins are Parco archeologico di Brixia Romana: https://www.bresciamusei.com/musei-e-luoghi/parco-archeologico/
Buy the combo ticket with the Museo di Santa Giulia because aside from it being a very interesting museum it sits on top of the old Roman baths so the basement is a series of in situ mosaiced rooms and some of the museum walls are actually Roman walls from the excavation.

South of there are yet more piazzas like Piazzale Arnaldo but this felt like more of hipper night club kind vibe in the area so I returned to the old town.

You can walk the very uphill path to Castello di Brescia or taxi/bus to it. https://www.bresciamusei.com/en/museums-and-venues/the-castle/

A fair amount of public art in the piazza areas of Brescia as well - say "Hi" to hovering rhinoceros if you go.

I'm apparently alone in this but I preferred Brescia to Padua/Padova. Padova has amazing churches but I preferred the ruins and vibe of Brescia more even though the city populations/sizes are very similar.

Have a great trip whatever you do,
=Tod