Where to spend 5 Nights

I've only been in Milan once. I spent 4 nights (so 3 days) there in the Hotel Berna near the train station:
https://hotelberna.com/en/

I'd love to go back for a longer time, so you can probably guess that my choice would be to stay in Milan and use it as a home base, possibly not taking any day trips at all. Below I hope I've provided some helpful links for visiting Milan. You can also find much more info online about the city including an especially thorough Wikipedia article.

I'm assuming that your flight departs from Milano Malpensa is not at 0:dark:30:
https://www.milanomalpensa-airport.com/it/

If so, it's useful to stay near Milano Centrale Train Station:
https://www.italiarail.com/train-station/milano-centrale-train-station

That makes it easy to catch the train or take a shuttle bus to the airport. Either will take at least an hour. If you do decide to do day trips on your own, it's also convenient for that, although the whole process could take about 2 hours each way to Lake Como or Bologna. If you stay that far away as a home base, I'd recommend planning to spend your last night at one of the airport hotels.

I haven't spent any time in Bologna, but my husband and I did spend 3 nights (2 days) at Lake Como. We stayed in Varenna at the Hotel Olivedo right across the street from the ferry dock:
http://www.olivedo.it/en/hotel-olivedo/

We had a lovely corner room with a balcony and great views. Although there are some things to do and see around the lake, we didn't do much except eat, walk around and take the ferry around the lake twice using a day pass.

Here's Rick Steves detailed information about Milan: https://www.ricksteves.com/europe/italy/milan

Two of the things I did are described here:
https://www.ricksteves.com/watch-read-listen/read/articles/milan-italy-top-sights

I took the Milano Metro from between the hotel and train station to the Piazza del Duomo and back to the hotel.

Besides taking the elevator up and exploring the Duomo roof, I also visited the Archeological Area under the Duomo. I did not visit the museum. This is the official Duomo website where you can purchase a variety of different kinds of tickets:
https://www.duomomilano.it/en/

Beyond some of the things I didn't have time to see or do in Milan last time, if I get to go back I want to eat at this place that Stanley Tucci featured in one of his programs, Osteria del Treno:
https://www.osteriadeltreno.it/

And, although I'm not a big foodie, that would be a major impetus to return to Milan.

Thanks so much Lo, so much great info!!

I suspect much has to depend on what you would like to see and do. Bologna, as a base, gives you many options. Ravenna and Parma are easy day trips. Lake Como is gorgeous and Varenna is a great base, especially if you want to explore the eastern shoreline.

Lake Garda would be another suggestion. The northern part is mountainous and very different from the southern part of the lake. From the southern part you can train to Verona for a day trip.

If you like to hike, the Dolomites may be another choice. Need to make sure the lifts are running at that time. Maybe a couple of nights in Bolzano and a few nights in in Alta Badia

Padua is another option. From there you can train to Venice for a day, Verona for a day,

Who doesn't like Bologna and surrounding areas. If you do decide on Bologna and you like to eat, check out Italian Food Days all day tour. You will visit a Parmigiano Reggiano cheese, Balsamic Vinegar and Prosciutto ham factories as well as a 2 hour lunch.

There are so many choices to choose from. Enjoy

You will want to consider how long the transfer is to one of the places you might enjoy. Nice to Bolzano, for example, is over 9 hours by train and you won’t even be in the mountains yet. Plus, it’s not really in season in the mountains yet the end of May. Nice to Milan is toughly 5.5 hours then another hour to Lago di Como at Varenna. You can do a lot 8n and from Milan with day trips. Play around with transit times and see what you are up for in travel days. Rome to Rio is a good starting point.

BTW, I like Genoa based on a 1 night stay a few years ago but not sure 4 or 5 nights is warranted.

I love Bologna, but train time from Nice Ville is 7 hours.

I would pick a place on the train route from Ventimiglia to Milano, ideally the Grand Hotel in San Remo. Then Savona or Pavia. Following train route shows the possible day trips:

https://www.e656.net/orario/treno/745.html

Interesting note about the town of Savona. In the Piazza Mameli there is a statue, a memorial honoring the 21 local men who died in WWI. Every evening at 6PM bells ring 21 times and everyone [foot traffic and vehicles] stops.

Also Savona has its own Sistine Chapel:

https://tinyurl.com/ywc74b8m

I'd select Stresa or Verona. Bologna might make my list, but Genoa & Parma would not.

I was in Genoa a few times as a kid visiting family, but was never impressed with the city.

Regarding Milano, the three stations with trains to the airport are Centrale, Cadona and Porta Garibaldi; advisable to be at one of these 4 hours before the flight. For an early morning departure, best to be at a Malpensa Hotel the night before [e.g the Villa Malpensa with its excellent restaurant].

demarl, is anything standing out so far? Have you looked at Turin?