Wine and Italy

Italy is huge. You probably need to look at the different regions and figure out what interests you the most.

Here’s a previous post on Amalfi coast area:
https://community.ricksteves.com/travel-forum/italy/amalfi-coast-questions-cc96896a-f4ec-486a-83cd-4b8184e4d484

Here’s a link to the Italy guides for purchase on Rick Steves Travel Store.

https://store.ricksteves.com/shop/guidebooks/italy

I'm confident they'll lead you to the answers to your questions.

Happy research and planning!

Italy is my favorite foreign country. I have been there about a dozen times.
There are so many great places to see.
Rome is wonderful, but if you are interested in smaller cities, here are a few options:

1)The Amalfi Coast is just south of Naples, Pompeii, Sorrento and Capri. Don't miss all these places if you go to the AC.
You don't need to rent a car, but do your research in how you go from point A to B.

2) Tuscany and Umbria are the regions in the middle of Italy, around Florence and SE of Florence.
There are many wonderful smaller cities and towns in these to areas,
Florence deserves 3-4 days itself. Siena is a great place to stay to do day trips to many places in Tuscany.
Pisa and Lucca are in Western Tuscany, and there are more great places to visit. San Gimignano is a must.
https://www.tripadvisor.com/Attractions-g187893-Activities-Tuscany.html

https://www.earthtrekkers.com/best-things-to-do-in-tuscany/

For Umbria, don't miss Assisi, Perugia, Spoleto, Gubbio and Orvieto. There is more.
https://www.tripadvisor.com/Attractions-g187904-Activities-Umbria.html

https://theculturetrip.com/europe/italy/articles/the-10-most-beautiful-towns-in-umbria

Other areas of Italy are great, like the north around Milan and the lakes near Switzerland. Also, Venice, Bologna and Ravenna.

The Amalfi Coast will be mobbed in June. Not sure that is what you have anticipated. It has sadly been ruined by the crowds, and compounded by the poor transportation infrastructure, is just not a relaxing area to visit during the spring, summer, or fall.
We really do enjoy Venice, as there are so many quiet neighborhoods that do not have the crowds of St Mark's Square and Rialto Bridge areas.
Perhaps you would enjoy Tuscany?
June will be hot and humid, so compare prepared.
I would advise making a decision asap, as summer lodging options book up early.
Have a great trip!

more or less take time to "immerse" ourselves among locals,

on the Amalfi Coast in June you will be immersed in tourists with not room to swing a cat.

You have loads of time to prepare. For those encouraging rapid reservations note that the trip is next year (mid-June 2027)

Oops 2027- I missed that, thanks, Nigel!

Don't dismiss Rome outright . I surprised myself by how much I enjoyed the city. To walk among the ancient monuments while on a stroll is a lovely history lesson and you haven't even stepped foot in the wonderful museums. Fantastic restaurants, enotecas, gelaterias. And lots of nearby places for a day trip.

Consider planting yourselves in the walled city of Lucca. Easy day trips by train or bus to Florence, Cinque Terre, Pisa, Castelnuovo di Garfagnana, Pistoia, ...

Hi, you put wine in your title, but I’m not sure what your interest in wine is. There are several excellent wine regions in Italy. A few of my favorites include: the Alto Aldige for whites like Pinot Grigio and Pinot Bianco, Tuscany for Barolo and Sangiovese, Sicily (especially Etna region) for elegant and unusual reds and whites. Anyway, this could help steer your itinerary if wine is an important part of it. Note that the best wineries have limited tasting appointments and it is a bit more formal (and often includes food or experiences) than in the US so plan and book ahead!