This paper presents an approach for selecting the next best base position for a climbing robot so as to observe the highest information gain about the environment. The robot is capable of adhering to and moving along and transitioning to surfaces with arbitrary orientations. This approach samples known surfaces, and takes into account the robot kinematics, to generate a graph of valid attachment points from which the robot can either move to other positions or make observations of the environment. The information value of nodes in this graph are estimated and a variant of A* is used to traverse the graph and discover the most worthwhile node that is reachable by the robot. This approach is demonstrated in simulation and shown to allow a 7 degree-of-freedom inchworm-inspired climbing robot to move to positions in the environment from which new information can be gathered about the environment.