For what reason is Shakespeare's The Taming of the Shrew (mainly) set in Padua?
why did shakespeare choose this setting? what was/is special about padua that relates to the play?
was it a city popular for good educational standards then?
i'd really appreciate any ideas!
It is also possible that Shakespeare chose an Italian setting (Padua for Baptista's house and Verona for Petruchio's) because he wanted to suggest a setting appropriate for characters reminiscent of commedia dell' arte. Commedia was simply an Italian theatrical comic form with stock characters (young lovers, old miserly man, crafty servants) that was quite popular in Shakespeare's day. Much about the plot of Shrew emulates common lazzi (comic bits of plot) found in Commedia.
You shouldn't concern yourself too much with why Padua or Verona, since a play's setting is really quite malleable. Unlike a novel, a play isn't written with a setting frozen in time and place. The actual time and place of setting is something usually decided upon by those producing and performing it. So, if you see the play performed live or you watch productions of it that have been filmed, you'll see many choices of time and place.
Even the modern film/TV show inspired by Shrew, 10 Things I Hate About You proposes Padua High School as its setting, a setting that could definitely work for a production of the play.
You are right to say that Padua was well known for education. It was the site of the first medical school in Italy.
As far as why Shakespeare set the play in Padua, I can't say why Padua in particular. But you should ask yourself this -- why did he set so many plays in Italy? Outside of the histories, it's not like the plays had to be set in Italy.
The most usual answer is that it was dramatically better to set plays somewhere exotic. When plays were set in exotic locations it could help put the audience in an imaginative frame of mind. It would also let them think about the characters without trying to make them fit into their own ideas about life. In other words, if the characters were English people might think "I don't know anyone who acts like that!" But if they're Italian you don't have that problem.