If you intend to move there there are income tax breaks for those foreigners moving to municipalities of less than 20,000 residents in the southern regions (Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria, Sicily, Sardinia). The income tax would be a flat tax of 7% for 10 years.
However I think you intend to stay only for extended vacations, therefore the limit is 90 days over 180 day rolling period. In that case, having a house that you can enjoy only 3 months a year may not be worthwhile. You both qualify to acquire Italian citizenship even without moving there. If your husband lost his citizenship there is a procedure for reacquisition, and it is rather simple. Once he becomes a citizen, you as a spouse of an Italian citizen for at least 3 years, can immediately apply for citizenship as well (without moving there). The bureaucratic process takes almost two years and since 2020 it requires a basic knowledge of the Italian language. My wife went through it, but at the time there was no need to know any Italian. If you both become citizens, you can stay longer than 90 days. Just consider however that if you stay over 183 days in a calendar year you become a tax subject and you’d be liable to pay taxes there. But of course if you stay a little longer than 183 days they won’t find out that easily because when you enter Schengen with an Italian passport they don’t keep track of your wherabouts.
There is a property tax on second homes (property tax does not apply on the first residence home), which is not high compared to NJ, but should be considered. There is also a local tax called TARI which covers street lighting and garbage, which amounts to under €150 a year for a house of that size. In addition to that you need to pay utilities, which on second homes are higher than on first residence homes. Just because you are not there it doesn’t mean that bills stop. Gas, electricity, water, have fixed amounts that are billed every two months (billing cycles in Italy are generally bimonthly) even if your consumption is zero.
You can open a bank account as a foreign resident, but not all banks allow this. Many don’t like to open accounts to US citizens because of FATCA (Foreign Account Tax Compliance Act) of 2010. Banca Intesa, my bank, allowed me to open one even after FATCA, although I’m an American with foreign residence. There are however restrictions on the investments you can make, due to the interbank treaty between the US and other countries related to FATCA. Of course you could buy a house in Italy using your US account, but once you have the house you need an Italian account to pay the various bills and taxes (also automatically) otherwise you spend a fortune in internstional bank transfer commissions to your bank every month.