As COVID-19 becomes a dangerous pandemic worldwide, there is an urgent need to understand all aspects of it through data visualization. As part of a larger COVID-19 response by KAIST, we have worked with students on generating interesting COVID-19 visualizations including demographic trends, patient behaviors, and effects of mitigation policies. A major challenge we experienced is that, in an open world setting where it is not even clear which datasets are available and useful, generating the right visualizations becomes an extremely tedious process. Traditional data visualization recommendation systems usually assume that the datasets are given, and that the visualizations have a clear objective. We contend that such assumptions do not hold in a COVID-19 setting where one needs to iteratively adjust two moving targets: deciding which datasets to use, and generating useful visualizations with the selected datasets. We thus propose interesting research challenges that can help automate this process.