The correct answer is $\boxed{\text{A}}$.
The departure of two places is the difference between their longitudes, expressed in degrees. In this case, the longitudes of the two places are 93° E and 97° W, so their departure is 93° – 97° = -4°. One degree of longitude is equal to 60 nautical miles, so the departure of the two places is 4° * 60 nautical miles/degree = 240 nautical miles. However, the question asks for the departure in nautical miles, not degrees. To convert from degrees to nautical miles, we multiply the departure in degrees by the cosine of the latitude. The latitude of the two places is 60° N, so the cosine of the latitude is $\cos(60^\circ) = \frac{1}{2}$. Therefore, the departure of the two places in nautical miles is 240 nautical miles * $\frac{1}{2} = 120$ nautical miles.
Option $\text{B}$ is incorrect because it is the departure of the two places in degrees, not nautical miles. Option $\text{C}$ is incorrect because it is the distance between the two places, not the departure. Option $\text{D}$ is incorrect because it is the distance between the two places in nautical miles, but it is too small.