I was going to suggest something like @CD in DC mentioned. Modena has a nice old town section and is a good walkable city. It is also in the center of Emilia Romagna which features many types of specific food production. It is the capital of balsamic vinegar production, of course, Reggio Emilia for cheese and Parma for the ham production. Bologna - the collecting place for all these things is 30 minutes away by train. It also has the Albini marketplace to visit as well as good restaurants - including the 3 Michelin starred Osteria Francescana if that interests you.
This brings up an important point - are you restricted to public transportation or are you willing to rent a car for part of your trip? Farm visits are technically difficult without transportation since they are rural by definition. If you are stucking with public transportation you can arrange tours out to cheese and balsamic production places but getting there on your own without a car will be a challenge. Areas that want to highlight food production - like Modena and Bologna - make this easier because food farm tours are part of their tourist appeal.
Bologna is the center of all these things and the center is walkable and is the center of public transportation, but I don't know if a big city is something you would consider as a place "go slow". Populationwise Parma isn't all that much bigger than Modena but it feels like a much bigger, more serious city than Modena which as a smaller town feel in the old center at least.
Rimini area on the Adriatic coast is the most easily reachable beach area. The coast of northern Tuscany and southern Liguria - Viareggio and La Spezia specifically - can be reached by train but it takes longer because of the mountains and train changes, but is doable if you are willing to spend twice as long.
Two other slightly less specific suggestions are the Lucca and Salerno areas.
Lucca is a great "go slow" food town and has easy 17 minute access to Viareggio beaches on the train and is rural enough that walking and nature are pretty close. They have the usual Tuscan productions like wine and olive oil and some organic farms but agriculture is not part of their attraction so you'll need to work harder to put together tours or visits.
Salerno is a beach city itself and has ferry and bus access to the Amalfi coast as well as access to Naples (the opposite of going slow), Pompeii, Paestum and the nearby Buffalo milk production farms. The area around Naples is highly agricultural and produces things like the famous tomatoes raised in volcanic soil but you would need to investigate local tours or access beyond the buffalo farms. Salerno offers both sea and land based foods unlike many port cities in Italy.
Hope that helps, have a great slow trip,
=Tod
