Disclaimer: I'm no longer super familiar with scholarship on medieval Italy. As long as you don't need super cutting-edge scholarship, though, John Julius Norwich's A History of Venice is hands-down my favorite non-academic book on history. (It was also probably the single most influential book in convincing me to take up history as a career.) It goes until the fall of the Venetian Republic, so quite a ways after the end of the Middle Ages, but there's quite a bit of medieval stuff, too. It really stands out for readability and style - or at least my definitions of both those qualities - so maybe it would work for 'interesting?'

Check the wiki reading list. I put a few down there. https://www.reddit.com/r/AskHistorians/wiki/books/europe#wiki_middle_ages. Look under the political and economic sections. Waley's Italian City Republics is the standard undergraduate textbook and has been updated several times and each chapter contains sections with suggestions for further reading. UPenn has a rather nice collection of sources if that's your jam. Jones's Commune to Signoria is the standard history, but it's like 100 dollars and may be a bit much.

As far as popular histories go, if that's what you're looking for, Madden's recent Venice, a New History is quite good, it's in the wiki. Epstein's history of Genoa and Najemy's history of Florence are also their and both are the standard English narrative of their respective subjects.

Oh, and Cities of God by Thompson is brilliant.