Best cities for retirement in Italy

You are asking a lot as Umbria, Tuscany, and La Marche all are within your remit and they are all VERY DIFFERENT REGIONS.  Italy is a vast area of many differing experiences.

La Marche is extremely mountainous to the eastern seaboard & central region. This means few rail or road links to major airports or rail hubs and so much cheaper than other areas. Semi-wild so a car is essential and a good understanding of local laws and reconstruction permits as this is a very rural area. An area for the adventurous and those with long investment plans,
Umbria bordering the wilds of La Machche and expensive Tuscany is often overlooked ( the locals are not so sorry) as this small province offers all the tranquility and rural of its Northern neighbor but has all the road air and rail links to all of Italy without the hustle and bustle of the cities. It has the gently rolling hills, the cypresses, truffles, pasta, meats, and grains indigenous o the area. A good blend of the meat orientated NORTH & the 'POOR' peasant menu the south. Good honest food locally produced and well presented at  REASONABLE COST cities with high tourist numbers take advantage so look for man in overalls and eateries on the edge of town for good honest meals.

We take advantage of the good rail and road links to explore the cities and towns, choosing seasons, events, sagas concerts for our visits. Each comune has a tourist office to give advice about events, parking, eating & points of interest, so it is essential to ask locally of the tourist office who are always helpful in their area.
Also, look at the posters along the roads in town at parking venues and in bars for local events also as the locals work on word of mouth any missing information is just a cafe away...

Having explored the other regions we are one with the agricultural, slow pace of life in central Umbria producing flavorsome organic produce that we like. We moved to \iluy o experience a slow pace of life, one determined by the seasons and have not been disappointed but not everyone likes the rural ideal.

High living, shopping is your ideal look to Milan and Rome or other cities, for peace and quiet the countryside just off the major routes will give the locations you are looking for, maybe only 15 minutes so go out of your box to search, all too  often we are restrained by the unknown and miss opportunities  my minutes due to lack of small bravery....CARPE DI EM....  'go for it  as you live once and regret for eternity'' if given the time and opportunity.




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I think Italy is a great place to retire for a lot of reasons and each region has its advantages and flows. I think before making a final decision you need to consider your interests, activities and, of course, finances. M.Hunt in his reply mentioned Tuscany, Umbria and Marche, 3 great regions but there are 17 other to choose from each one of them wonderful as well.   
The following suggestion are based on my experience of having lived in medium size cites of the north but  have traveled throughout Italy  and are more general in nature.

Regarding interests, I assume gastronomy is  very much high  on your list. My experiences having traveled from the toe to the to top of the boot,  has been great no matter where I was. Customs varying from region to region and , at times, even withing a region dictate gastronomy. This does't mean that you will not find a good pizza in the north. It is just that I follow the golden rule of " when in Rome, do  as  Romans do"  .  Culture events will be more available in large (particularly in the North) cities. 

Regarding activities, the Alps bordering the top of the boot  and Apennines  running down the boot offer great hiking and snow sports as well as unforgettable views . I resided in Lecco and Verona in the colder months due to my love of skiing and hiking which were easily accessible from both of those cities.  If you like the sea, I like the west coast more than the east and of course the islands. Having said this I will be spending the summer in Ancona because I couldn't find an apartment on the other coast matching my needs. If you like sailing, the northern  portion of Sardinia and the Aeolian Islands are a must. 

Regarding transportation,  a car is indispensable if you decide to reside in a small village  or  in the outskirts of medium size cities which are not on the main rail or bus lines. The west coast is better served by rail service than the east coast . In the interior , the north has better transportation than the rest of Italy.  My decision to reside  in Verona and Lecco was driven by my decision not to have a car and these cities being well connected to the rest of Italy by air , train and bus services. One note, there are also bus companies serving Italy (i.e., FlixBus) . These  offer great deals connecting large, medium and small cities. So, when considering a place to reside , you will definitely to consider transportation  even for your weekly or possibly daily  grocery shopping. 
Regarding Finances, the real estate in the northern section of Italy is more expensive than the rest of Italy due to its industrialization. Conversely , the southern section is the least expensive. Of course, real estate in  areas heavy with tourists will  be more expensive anywhere in Italy.

A couple of other matters that you may need to consider prior to retire full time in Italy. Moving to and residing in Italy is not a smooth process (think  bureaucracies) and I heard that you must prove  you are financially able . Also , taxation on income may be an issue as well as health insurance (by the way on this matter, healthcare in the north is  better than the south from a personal experience).
As I mentioned, my suggestions are very general in nature and are based on my experience, Others may have  different views based on their experience. But I think everyone will agree that Italy is one of the best country to retire to. Hopefully, the above helps.
Buona fortuna