The COVID-19 health emergency and restrictive measures have increased psychological problems, particularly anxiety and depression, in the general population. However, little is known about mental health conditions and the possible risk and protective factors of specific population groups, such as institutionalized vs. community-dwelling elderly. We investigated the abovementioned aspects in a sample of 65-89-year-old people during the third wave of COVID-19 in Italy. We employed a sociodemographic survey and four questionnaires on health-related quality of life (SF-36), loneliness (UCLA), spirituality (FACIT-Sp), and anxiety/depression (HADS). Our findings suggest that the physical, psychological, and spiritual well-being of the elderly had not been seriously impaired by the events related to the pandemic, although most of the participants reported a worsening of their social life and a moderate/high fear of COVID-19. In regression analyses, these two latter aspects turned out to be predictors of higher anxiety, while spiritual well-being and the possibility to get out of the house/institution emerged as protective factors against anxiety and for preserving quality of life, respectively. Our findings help refine the picture of the condition of the elderly in the aftermath of the pandemic, giving some hints about how to continue supporting their well-being and quality of life.