How did those living both inside and outside of Chicago in 1890 view the city?
You asked two questions, and the second one seemed to be the most comprehensive and helpful. The Devil in the White City by Erik Larson is an account of the World's Fair in Chicago in the late 1890s. In it we discover that Chicago was seen as a lawless, dirty, heathen, and backwards place by the presumably more cultured and refined people in the East--and they were the ones who mattered at the time.
New York was in contention for the site of the Fair, and the people of New York were confident they would be chosen over such a wild and undeveloped place as Chicago. When that did not happen, the people of Chicago--and particularly the architect Burnam--found themselves an enemy of the powerful city. None of the architects there would agree to work on the project, even though in the end it would be a reflection on their country. They were bitter enough about the snub to let Chicago--and America--fail. Finally Burnam manages to get some of them to work with him, but they--like most of the East--still saw Chicago as an unworthy site to display America's best.
People in Chicago were, indeed, a little overwhelmed at the scope of the project, and it takes them a while to really get the project settled and going. They moved the site to edge of the water, which in many ways shows their lack of understanding about the significance of the Fair. The city did prepare for its guests in the best way it knew how, but it was still basically a city of mud and squalor. Once the White City came to life, the city of Chicago began to take pride in their grand accomplishment.
In general terms, the East was right about the physical conditions of Chicago. It was a rather wild and dirty place; however, in terms of talent and ability, the East underestimated the talents and abilities of these Midwesterners. When the world came to Chicago, it was met with an unexpected refinement and hospitality (with the glaring exception of the killer Holmes) which made their World's Fair experience even richer.