Recent studies indicate that robotic coaches can play a crucial role in promoting wellbeing. However, the real-world deployment of wellbeing robots raises numerous ethical and socio-technical questions and concerns. To explore these questions, we undertake a community-centered investigation to examine three different communities' perspectives on using robotic wellbeing coaches in real-world environments. We frame our work as an anticipatory ethical investigation, which we undertake to better inform the development of robotic technologies with communities' opinions, with the ultimate goal of aligning robot development with public interest. We conducted workshops with three communities who are under-represented in robotics development: 1) members of the public at a science festival, 2) women computer scientists at a conference, and 3) humanities researchers interested in history and philosophy of science. In the workshops, we collected qualitative data using the Social Robot Co-Design Canvas on Ethics. We analysed the collected qualitative data with Thematic Analysis, informed by notes taken during workshops. Through our analysis, we identify four themes regarding key ethical and socio-technical questions about the real-world use of wellbeing robots. We group participants' insights and discussions around these broad thematic questions, discuss them in light of state-of-the-art literature, and highlight areas for future investigation. Finally, we provide the four questions as a broad framework that roboticists can and should use during robotic development and deployment, in order to reflect on the ethics and socio-technical dimensions of their robotic applications, and to engage in dialogue with communities of robot users. The four questions are: 1) Is the robot safe and how can we know that?, 2) Who is the robot built for and with?, 3) Who owns the robot and the data?, and 4) Why a robot?.