We present BubbleView, a methodology to replace eye-tracking with mouse clicks. Participants are presented with a series of blurred images and click to reveal "bubbles" - small, circular areas of the image at original resolution, similar to having a confined area of focus like the eye fovea. We evaluated BubbleView on a variety of image types: information visualizations, natural images, static webpages, and graphic designs, and compared the clicks to eye fixations collected with eye-trackers in controlled lab settings. We found that BubbleView can be used to successfully approximate eye fixations on different images, and that the regions where people click using BubbleView can also be used to rank image and design elements by importance. BubbleView is designed to measure which information people consciously choose to examine, and works best for defined tasks such as describing the content of an information visualization or measuring image importance. Compared to related methodologies based on a moving-window approach, BubbleView provides more reliable and less noisy data.