The rock described, which contains individual black and white crystals that are easy to see, suggests that it is likely an igneous rock, specifically a type that has a coarse-grained texture. Coarse-grained textures typically indicate that the rock cooled slowly, allowing larger crystals to form.
Given that it's found in an area that once had an active volcano, the most appropriate additional description would be:
exposed to air and water.
This implies that the rock has been subjected to weathering and erosion since its formation. The options "fine texture," "cooled quickly," and "cooled inside the volcano" do not fit well with the characteristics of the rock as described.