I don't believe the town where Grandma Dowdell lives is actually named in the book.  Joey describes going to her home on the train, "the Wabash Railroad's crack Blue Bird that left Dearborn Station every morning, bound for St. Louis...Grandma lived somewhere in between, in one of those towns the railroad tracks cut in two".  If you look on a map, Dearborn Station is in Chicago, which is in the northeastern corner of Illinois.  St. Louis is on the eastern border of Missouri, where it intersects the southwestern border of Illinois.  The town, then, would be located somewhere in central Illinois. 

To the children, who are used to the hustle and bustle of the big city, the town seems hopelessly "slow".  It is "only a short block of brick buildings:  the bank, the insurance agency, Moore's Store, and The Coffee Pot Cafe, where the old saloon had stood...they still had the tin roofs out over the sidewalk, and hitching rails...most farmers came to town horse-drawn, thought there were (some) Fords".  At first, the children think "there (is) nothing to do and nobody to do it with", but they soon discover that, living with their grandmother, there is never a dull moment (Chapter 1).