Since no one has mentioned it yet, The Bagel Table on Guest St. in Brighton. Classic bagels, just the right texture.

Many organizations at Harvard have their own series of public talks. Examples are:

• Forums at the Institute of Politics (part of the Kennedy School of Government)
• Talks at the Radcliffe Institute for Advanced Study
• Norton Lectures featuring award-winning writers, musicians, filmmakers, etc.
• Distinguished Lecture series at Institute for Applied Computational Science (open to public, but intended for a technical audience)

There are probably many more events run by Harvard's other individual schools, departments, and institutes.

Harvard has two pools but you have to be an affiliate (employee, student, etc.) or family member to get a membership. So not really public.

There is a public outdoor pool at Magazine Beach, although it's only open in warmer months for obvious reasons.