A numerical algorithm is used to generate two-dimensional surfaces defined by x3 equals (zetz) (x), with x equals (x1, X2), where (zetz) (x) is a single-valued function of x that constitutes a zero- mean, stationary, isotropic, Gaussian random process defined by the properties <(zetz) (x)> equals 0, <(zetz) (x)(zetz) (x1)> equals (sigma) 2W(x - x1), and (sigma) 2 equals <(zetz) 2(x)>. The angle brackets here denote an average over the ensemble of realizations of the surface profile function (zetz) (x). The results are used to compute the probability density P1(x)[P2(x)] that the nearest maximum (minimum) to a given maximum (minimum) is at a distance x from the latter; and the probability density P3(x) that the nearest minimum to a given maximum is at a distance x. Results are presented for random surfaces defined by surface height autocorrelation functions W(x) equals exp(-x2/a2), a2/(x2 + a2), and 2[(k22 - k12)x2]-1[k2xJ1(k2x) - k1xJ1(k1x)], where J1(z) is a Bessel function. Results are also presented for a novel type of one-dimensional random surface used in recent experimental studies of enhanced backscattering.