When combined with machine learning, the black-box analysis of fitness landscapes promises to provide us with easy-to-compute features that can be used to select and configure an algorithm that is well-suited to the task at hand. As applications that involve computationally expensive, stochastic simulations become increasingly relevant in practice, however, there is a need for landscape features that are both (A) possible to estimate with a very limited budget of fitness evaluations, and (B) accurate in the presence of small to moderate amounts of noise. We show via a small set of relatively inexpensive landscape features based on hill-climbing methods that these two goals are in tension with each other: cheap features are sometimes extremely sensitive to even very small amounts of noise. We propose that features whose values are calculated using population-based search methods may provide a path forward in developing landscape analysis tools that are both inexpensive and robust to noise.