We investigate two new strategies for the numerical solution of optimal stopping problems in the regression Monte Carlo (RMC) framework proposed by Longstaff and Schwartz in 2001. First, we propose using stochastic kriging (Gaussian process) metamodels for fitting the continuation value. Kriging offers a flexible, non-parametric regression approach that quantifies approximation quality. Second, we connect the choice of stochastic grids used in RMC with the design of experiments (DoE) paradigm. We examine space-filling and adaptive experimental designs; we also investigate the use of batching with replicated simulations at design sites to improve the signal-to-noise ratio. Numerical case studies for valuing Bermudan puts and max calls under a variety of asset dynamics illustrate that our methods offer a significant reduction in simulation budgets compared with existing approaches.