This paper reports on an integrated navigation algorithm for the visual simultaneous localization and mapping (SLAM) robotic area coverage problem. In the robotic area coverage problem, the goal is to explore and map a given target area within a reasonable amount of time. This goal necessitates the use of minimally redundant overlap trajectories for coverage efficiency; however, visual SLAM's navigation estimate will inevitably drift over time in the absence of loop closures. Therefore, efficient area coverage and good SLAM navigation performance represent competing objectives. To solve this decision-making problem, we introduce perception-driven navigation, an integrated navigation algorithm that automatically balances between exploration and revisitation using a reward framework. This framework accounts for SLAM localization uncertainty, area coverage performance, and the identification of good candidate regions in the environment for visual perception. Results are shown for both a hybrid simulation and real-world demonstration of a visual SLAM system for autonomous underwater ship hull inspection.