Local field enhancements in aperiodic arrays of gold nanospheres are studied. The arrays are based on three aperiodic tilings of the plane which display 5, 7, and 8 fold rotational symmetries that are not possible in conventional periodic arrays. Electromagnetic (EM) field calculations are based on the analytical generalized Mie theory (GMT). It will be shown that despite the fact that aperiodic arrays are much sparser than periodic arrays, they display larger local field enhancements. Also due to their higher degree of rotational symmetry, the field enhancements are less dependent on the polarization of the incident radiation. Finally, it will be shown that local fields can be further enhanced by optimally placing perturbing spheres within the prototiles that comprise the aperiodic arrays.