Your local city college may or may not offer free classes (in San Francisco, you just need to show proof that you live in the city with some legal status).
Some public transportation is free for certain groups (youth and folks experiencing homelessness can get free passes here).
"First X of the month" at the zoo/a museum/whatever --- lots of venues have free events.
A jog, bike ride, hike --- lots of great stuff outside!
I live in the Philly area. Senior citizens can use SEPTA (buses and commuter trains) for $1 a ride.
I second the biking ... but that shit ain't free. Even used bikes cost some money to buy and maintain, and brand new bicycles are solidly in the "insane" category these days.