With the push for transparency and open data, many datasets and data repositories are becoming available on the Web. This opens new opportunities for data-driven exploration, from empowering analysts to answer new questions and obtain insights to improving predictive models through data augmentation. But as datasets are spread over a plethora of Web sites, finding data that are relevant for a given task is difficult. In this paper, we take a first step towards the construction of domain-specific data lakes. We propose an end-to-end dataset discovery system, targeted at domain experts, which given a small set of keywords, automatically finds potentially relevant datasets on the Web. The system makes use of search engines to hop across Web sites, uses online learning to incrementally build a model to recognize sites that contain datasets, utilizes a set of discovery actions to broaden the search, and applies a multi-armed bandit based algorithm to balance the trade-offs of different discovery actions. We report the results of an extensive experimental evaluation over multiple domains, and demonstrate that our strategy is effective and outperforms state-of-the-art content discovery methods.