(1) Background: To describe sleep quality, eating behaviour and alcohol, tobacco and illicit drug use among healthcare staff in a Spanish public hospital. (2) Methods: Cross-sectional descriptive study examining sleep quality (Pittsburg Sleep Quality Index), eating behaviour (Three Factor Eating Questionnaire (R18)), tobacco and drug use (ESTUDES questionnaire) and alcohol use (Cut down, Annoyed, Guilty, Eye-opener). (3) Results: 178 people, of whom 87.1% (155) were women, with an average age of 41.59 ± 10.9 years. A total of 59.6% of the healthcare workers had sleep problems, to a greater or lesser degree. The average daily consumption was 10.56 ± 6.74 cigarettes. The most commonly used drugs included cannabis, occasionally used by 88.37%, cocaine (4.75%), ecstasy (4.65%) and amphetamines (2.33%). A total of 22.73% of participants had increased their drug use, and 22.73% had increased their consumption during the pandemic, with beer and wine accounting for 87.2% of drinks consumed during this period. (4) Conclusions: In addition to the psychological and emotional impact already demonstrated, the COVID-19 crisis has repercussions on sleep quality, eating behaviour and alcohol, tobacco and drug consumption. Psychological disturbances have repercussions on physical and functional aspects of healthcare workers. It is feasible that these alterations are due to stress, and it is necessary to act through treatment and prevention as well as promote healthy habits.