Which is better for a believing woman: to stay at home, or to travel and sightsee?

The fundamental principle is that it is better for a woman to remain in her home, based on the Almighty's saying: "And stay in your houses," and the Prophet's (peace be upon him) saying: "Indeed, a woman is awrah; if she leaves her house, Satan entices her, and she is closest to the mercy of her Lord when she is in the deepest part of her house." Her leaving her home is not better unless there is an overriding benefit. As for leaving merely for strolling and tourism, its least status is that it is permissible if it adheres to Islamic regulations, and it may be disliked or forbidden depending on the circumstances.