Interacting with strangers can be beneficial but also challenging. Fortunately, these challenges can lead to design opportunities. In this paper, we present the design and evaluation of a socio-spatial interface, SocialStools, that leverages the human propensity for embodied interaction to foster togetherness between strangers. SocialStools is an installation of three responsive stools on caster wheels that generate sound and imagery in the near environment as three strangers sit on them, move them, and rotate them relative to each other. In our study with 12 groups of three strangers, we found a sense of togetherness emerged through interaction, evidenced by different patterns of socio-spatial movements, verbal communication, non-verbal behavior, and interview responses. We present our findings, articulate reasons for the cultivation of togetherness, consider the unique social affordances of our spatial interface in shifting attention during interpersonal communication, and provide design implications. This research contributes insights toward designing cyber-physical interfaces that foster interaction and togetherness among strangers at a time when cultivating togetherness is especially critical.