rove
To wander around freely without a fixed plan or destination.
To rove means to wander from place to place without a fixed destination or plan. When you rove, you're moving around freely, exploring wherever your curiosity leads you. A group of friends might rove through a museum, stopping at whatever exhibits catch their eye. A cat might rove through the neighborhood, investigating interesting smells and sounds.
The word suggests pleasant, unhurried movement rather than aimless confusion. Someone roving isn't lost or frantically searching for something. Instead, they're enjoying the freedom to explore. Pirates and bandits were once called rovers because they roamed the seas or countryside looking for opportunities. Today, you might hear about a roving reporter who travels to different locations to cover stories, or security guards making roving patrols as they walk their rounds, checking different areas.
Your eyes can rove too. When you let your gaze rove across a detailed painting, you're looking at different parts without focusing on just one spot, taking in the whole scene at your own pace.