Joining the chorus of amateurs: Like an ice skater bringing in his or her arms, greater velocity will occur near the center of motion in a spin: Since momentum equals mass times velocity squared, the greater momentum will occur near the center. Thus the statement that greater strength will occur near the eye is rational. My erudite 12 year old states that the last side to hit is stronger, citing well written fiction (The Cay) - if so, second amateur suggestion, one might postulate that coriolis effect might augment the spin motions involved, but, like I said, we're not pro's.
Hurricanes tend to be strong on the onshore regions. The hurricane's forward motion combines with the storm relative wind velocity. Thus, it contributes to winds being stronger on the onshore side especially for faster moving hurricanes.