(1) Background: When the COVID-19 pandemic arrived, changes had to be made to several management aspects at our Pediatric Oncology Unit. We investigated how the families perceived these changes. (2) Methods: Two questionnaires were developed at the Pediatric Oncology Unit of the Istituto Nazionale dei Tumori in Milan in order to explore how the pandemic had affected the experience of patients who had been or were being treated at our hospital, as well as their families. These questionnaires were administered to three groups of individuals. (3) Results: Between July and October 2020, 120 questionnaires were administered to parents of patients. The impact of school closures and the impossibility of attending sports and social activities outside the hospital were regarded as important, and it was reported that 77.5% of parents judged social distancing to have affected their children. Regarding the changes introduced in the management of the ward and outpatient clinic, most parents’ opinions were positive. Differences in the opinions expressed by Groups 2 and 3 were statistically significant on the topics of relationships in the ward and staff workload. The aspect most negatively affected by the pandemic was the support that patients’ parents were able to give each other. Regardless of whether patients were treated before the pandemic or after the first lockdown, all parents indicated strong degrees of satisfaction with the care received and the organizational arrangements. (4) Conclusions: The results of our study point us in the right direction to further improve our daily work and better respond to the needs of our patients and their families.
