Safe Indoor Spaces Act This bill requires the Department of Health and Human Services (HHS) to establish a prize competition to incentivize the development of systems or devices that limit indoor transmission of COVID-19 (i.e., coronavirus disease 2019) and the virus that causes it. To be eligible for the prize, a system or device must meet certain criteria with respect to decreased viral transmission rates, scalability, and costs. In addition, HHS must establish a board comprised of experts in public health, education, small business, and engineering to advise on this competition.