The first public school was established in 1635. In which city was this school?
Boston Latin School in Boston, Mass. is the oldest public school in America. It was founded April 23, 1635.
It was started by Rev. John Cotton who wanted to create a school modeled after the Free Grammar School in Boston, England, in which Latin and Greek were taught. The school was publicly funded and the first classes were held in the home of Philemon Pormort, the school's master.
Believe it or not five of the 56 signers of the U.S. Constitution attended Boston Latin: John Hancock, Samuel Adams, Benjamin Franklin, Robert Treat Paine, and William Hooper.
Here is a link to a brief history of the school from its official site.