We have found some references to this area in literature:
69-71 Micklegate was once the office of 19th century railway engineer John Birkinshaw, whose clerk Richard Chicken was a famous eccentric regarded by many, including respected York historian Hugh Murray, as the inspiration for Mr Micawber. Chicken was living with his family in St Mary’s Row (now Victor St, near the Golden Ball). Dickens was a frequent visitor to York, staying with friends at first, later with his brother, who worked with Birkinshaw. The office closed in 1852 and has now been bought by York Civic Trust. Chicken gave his numerous children Latin names for numbers eg Sextus, the sixth boy. His letters are in York City Archives, and a memorial stone is at York Cemetery. See Murray, H. Mr Micawber in York, in York Historian 13 1996. His great-great-granddaughter, Sandra Midgeley, has created a website about Richard Chicken, here. You will see that he is said to have run a school in Swann St in the 1840s, but we have found no further evidence of this so far.
Wilkie Collins used Skeldergate as a setting in the plot of his novel No Name
Diarist John Evelyn (1620-1706) described the view from the Ouse Bridge in 1654.
Herman Melville, who wrote Moby Dick, came to York in the 19c, and was said to have been inspired by the remains of a sperm whale displayed locally
Henrietta Eliza Vaughan Palmer was born in Trinity Lane in Bishophill in 1856, and educated at Bootham House School. Writing under the pseudonym of John Strange Winter, she was a British novelist, and the founding president of the Writers' Club in 1892, and president of the Society of Women Journalists in 1901 to 1903. She set up the No-Crinoline League, but died in 1911. See also York: a Walk on the Wild Side, by Paul Furness and the York Alternative History Group.