Although the idea of owning such a property - a castle for example - is attractive to many people there are some issues that need to be addressed. Firstly what is the purpose of the purchase? If you are thinking of a private residence then you may be buying something of which you only use a small part - the rest of the rooms are left unused. Also castles and palazzi were not built to present day energy conservation standards and with high ceilings and drafty corridors your heating bill could well as high as one of the ceilings!
You may think about stripping the property and put in a modern interior and fix the exterior to stop the drafts. This can be done but the Italian national trust for architecture often have such buildings under their tutelage, and changes to the facades such as windows and doors are not allowed and any renovation has to be carried out in keeping with the original look, feel and materials.
If however you think a palazzi in the centre of town of a medieval castle in the Tuscan or Umbrian countryside could make an excellent 5 star country club then you could well be right. The amount of land that comes with theses estates is often large and a golf course, tennis courts and pools are all options. Also the size of such properties suggests a commercial venture or dividing the property into apartments, and selling off the individual apartments freehold. This is popular to many purchasers, it means they can turn up to their apartment without worrying about maitenance or if the place will be clean, as everything is taken care of by a management company.
Luxury modern villas on the Tuscan and Ligurian coast are always a good investment not only for capital growth but also rental income. Locations such as the Maremma in Tuscany or Sanremo on the Italian Riviera are places where bargains can still be had, but Portofino or Forte dei Marmi really are the most expensive locations on the coast - prices up to 14,000 euro per m2. As you can imagine you will be rubbing shoulders with national and international personalities and the villas are often in stunning locations, built with luxury in mind : marble everywhere (Massa Carrara is just down the road from Forte dei Marmi) and with every modern convenience. The Russian market like Forte dei Marmi.
You need to weight up not only the location but also the property itself. In the centre of Florence where are you going to park? Can I get workman who knows how to restore stone castles - usually yes, but they are becoming rarer!