Fairness in vaccination is not only important from a social justice point of view, but experience has shown that a fair distribution of vaccine proves more effective in public immunization by preventing highly-concentrated infected areas to form among the population. In this paper, we address fairness from two simultaneous points of view: equity and accessibility. Equity in our setting means that as far as possible, each demand zone should receive a fair-share of the total doses available. On the other hand, accessibility means that as far as possible, each demand zone should have equal travel distance to access their assigned vaccination site.