The circumference \( C \) of a circle is given by the formula:
\[ C = \pi \times d \]
where \( d \) is the diameter and \( \pi \) is approximately 3.14. To find the diameter, we can rearrange the formula:
\[ d = \frac{C}{\pi} \]
Given that the circumference \( C \) is 7,459 miles, we can substitute the values into the formula:
\[ d = \frac{7,459}{3.14} \]
Now, calculate the diameter:
\[ d \approx \frac{7,459}{3.14} \approx 2,375.79 \]
Therefore, the diameter rounded to the nearest hundredths place is:
\[ \boxed{2375.79} \text{ miles} \]