We introduce and study the problem of planning a trajectory for an agent to carry out a reconnaissance mission while avoiding being detected by an adversarial guard. This introduces a multi-objective version of classical visibility-based target search and pursuit-evasion problem. In our formulation, the agent receives a positive reward for increasing its visibility (by exploring new regions) and a negative penalty every time it is detected by the guard. The objective is to find a finite-horizon path for the agent that balances the trade off between maximizing visibility and minimizing detectability.We model this problem as a discrete, sequential, two-player, zero-sum game. We use two types of game tree search algorithms to solve this problem: minimax search tree and Monte-Carlo search tree. Both search trees can yield the optimal policy but may require possibly exponential computational time and space. We propose several pruning techniques to reduce the computational cost while still preserving optimality guarantees. Simulation results show that the proposed strategy prunes approximately three orders of magnitude nodes as compared to the brute-force strategy. We also find that the Monte-Carlo search tree saves approximately one order of computational time as compared to the minimax search tree.