As someone said, in that period of time (let's say close to 1250) the situation was very fragmented and there were the "Signorie" that we can translate as lordships.
The city Lordship represents institutional evolution of many city municipalities in center-northerner Italy around the half of XIII the century.
The stronger and rich lords succeeded therefore to obtain the faculty to designate to own successor, thus giving beginning to lordship's dynasties through the emperor authorization, that he often granted to the title it of Duke (behind strong compensations from the lords). They remained however working the communal institutions, although often they were limited to ratify the decisions of the lords. The more important were those of the De Medici, Gonzaga and Sforza. But also those of Della Torre, Visconti, Montefeltro, Estensi, Della Scala and Malatesta had, in various moments, remarkable importance.
This situation was made possible by the inability of the German monarchs to maintain control in the northern Italy and thanks to the little difficulty that the lords met for being recognized like legitimate authority.
Here's a list of lordships and locations:
For the imperial territory
Milano Della Torre, Visconti, Sforza
Verona Della Scala
And then in the Papal territory:
Ravenna Da Polenta
Urbino Da Montefeltro
I think it's important to cover all the italian territory, wich was full of interesting places, and what I have written it regarded only the lordships...