Perhaps the most popular thing to do in Valparaíso is simply to explore the streets on foot. The city wears its history and culture on its sleeve, so if you pick the right path (and there are many guides for walking tours of the city available), you're sure to find something interesting—a prison-turned-cultural park, for example, or a farmer's market that never seems to end.
The city, however, offers more traditional activities, as well. In Valparaíso you'll find several un-intimidating museums, a lively active harbor, a small multitude of art galleries scattered through the hills, and the nearby beaches of Viña del Mar for a day in the sun.