Which part of Europe? A lot of cities in Italy (and most of Europe) were Roman encampments (https://en.wikipedia.org/wiki/Castra) and they have a very square, ordinary layout I have always found boring.
I have always been fascinated by other cities when a road starts to curve or a square pops out of nowhere. Walking through London is much more interesting than it was in Milan.
I've never been there, but I heard there's a lot of planning in medieval italian city layout.
In particular Siena, which has detailed squares for trade, politics, full of simbolic features (e.g. the City Hall tower was built much higher than the church's to assure the government is perceived as superior).
Piacenza has the roman squared city center intact in layout[1], lots of other small towns as well, but the fact is the old town parts are likely too small to actually matter when you look at the whole city layout - hard to notice from just looking at the urban map!
then you have places like Turin that were built with a ruler [2]
AFAIK, Romans built their cities with streets following the N-S and E-W axes (Cardus and Decumanus) but, after, no medieval city continued with this style. Specially, in walled cities, the streets were appearing in a chaotic way.
My home city is Barcelona where, actually, a big part is designed as an orthogonal grid.... but it's still not the same. I think I would have enjoyed the game more if I knew how my cities were supposed to look like.
Although Milan has a circular layout that gravitates around the Cathedral, and the streets - especially in the center of the city - sometimes start to curve randomly or a square pops out of nowhere, just like you described :)
Maybe you where referring to Turin? (that has this exact square layout that makes me mad and lost sometimes - because nearby streets all seem the same)
I have always been fascinated by other cities when a road starts to curve or a square pops out of nowhere. Walking through London is much more interesting than it was in Milan.