“exceedingly great city.” The Hebrew uses the idiom, “a city great to God,” which if rendered literally would give the wrong impression to the reader. Using elohim as a descriptor, it means exactly what most English translations say, an exceedingly large city. The phrase, however, could also have the undertone meaning that the city was important to God, which it certainly was for His purposes in that day and age. Also, the word translated “great” can also mean “important.” So it seems very likely that there are a couple of meanings that God is trying to communicate built into a single sentence: that Nineveh was indeed a very large city, but also that it was important to God.
“of a three-day journey.” The Hebrew word translated “journey” in some English Bibles is mahalak (#04109 מַהֲלָךְ), and though it can mean “walk, journey, or “place to walk,” it can also refer to a visit (cp. NIV84, “a visit required three days”). Although many English translations say the city took three days to walk through (or walk around) even if a person could only walk 5 miles a day through the city, Nineveh was not 15 miles across, nor was it 45 miles in diameter (if a person walked 15 miles a day, a very reasonable amount for walking outside the city).
Nineveh was a very important city for politics and commerce, and social norms required lengthy greetings and introductions, as well as meals together and entertainment, so for a visitor to conduct serious business in the city could easily take three days (for a more detailed study of the translation “visit,” see Douglas Stuart, The Word Biblical Commentary: Hosea-Jonah).