Places to visit in the vicinity of Lake Orta after Village Italy tour

By near, how many hours of travel do you mean?
Train/bus or car?
How many days?
Where do you fly home?
nature/small village or city/culture?
Italy only or any interest in Switzerland?

I find myself drawn to Aosta, but I have limited experience in the north.

Thanks. In answer to your questions, considering northern Italy and Switzerland, would prefer train to car or bus, around 3 days extra but flexible, initially thought we would be departing from Milan, but would be flexible and consider leaving from elsewhere, including Geneva or Zurich (in another post, someone recommended that). More interested in nature/small villages since we fear cities would be packed in June. Our main consideration is avoiding hordes of tourists. I am assuming Venice in early June would be packed.

3 days or 3 nights?
3 nights only gives you 2.5 days- so I wouldn't want to spend a lot of time getting to wherever you choose.

Not sure there are too many places left that won't be busy in June.

You may have to decide on where you will depart from first- you wil likely need to be IN your departure city the night before so that's 1 night off of the 3 nights already

Lake Maggiore is just a bus ride away
Stresa is lovely- not quite as touristy as the other lakes and close enough to MXP that you can stay there the night before flight departure from Milan - there is a direct to MXP bus from Stresa ( it's actually closer to MXP than Milan is)

For most Switzerland locations seems like you'll spend the good portion of first day getting there- 5-6 hours?
Annecy- depart from Geneva- would need to stay in Geneva night before flight
Lucerne- depart from Zurich- you could stay in Lucerne night before- it;s a 1 hour train ride to ZUR

Just some thoughts

How about Turin? Yes it is a city and I am sure gets its fair share of tourists, but I always find it is easier to get away from the hubub in a mid range city like that. I hate crowds, and I would plan a visit there in early June without qualms.
For something smaller, I loved Alba, but I went without a car (and somewhat regretted it--we planned to hike but had rain). You can get there fairly easily, but then you might want to hire a driver for a day.

We went to Stresa on Lake Maggiore after the village Italy tour last month. Our guide arranged for a taxi to get us there from Lake Orta, and it was inexpensive and easy to get to the Milan airport by bus directly from Stresa. We stayed at La Luna Nel Porto, which was a splurge for us but absolutely fantastic— worth it, for sure! From Stresa you can take the small gauge train on a scenic ride to Italy and return via ferry. There are a lot of places you can get to by ferry, or you could just relax and enjoy Stresa. And make a dinner reservation at La Botte— very good food!

Sorry I meant to say you can ride the train to Switzerland!

I will tell you what we will be doing in September in a similar scenario. We will be on a hiking holiday with HF Holidays, staying in Verbania on Lago Maggiore for a week. One of our days will be spent hiking at Lago di Orta, which is nearby.

After the week of hiking, we will take the ferry up Lago Maggiore to Locarno, in Switzerland, and overnight there. Then we will take the Treno Gottardo, a scenic train over the Alps that goes to either Luzern or Zurich. We will take it to Zurich as we are flying out from there. But on the same route you have other options in Switzerland or also on Lago Maggiore.

For example, from the Orta Miasino station, you could take the train to Baveno on Lago Maggiore, a smaller and less touristed town than Stresa. Then take the ferry up the lake, maybe with an overnight in Cannobio, or not. End the ferry journey at Locarno. With the Treno Gottardo, you have the option of changing in the small hamlet of Flüelen to a lake boat up the lake to any of the smaller villages along the lake before reaching Luzern. Vitznau or Weggis would give you access to Rigi:

https://www.rigi.ch/en

You could even stay up on Rigi at Rigi Kaltbad (we enjoyed a night there several years ago). Then a night in either Luzern or Zurich before flying home from there.

Thanks much for all the great suggestions. If one stayed in Stresa, took the train to Locarno and then returned to Stresa by ferry, is that a day trip, or would it be better to do as an overnight in Locarno and return to Stresa the next day?