Someone else plans the occasion, states the location, and invites the entire city. All you have to do is attend and have fun. City marketplaces are another source of interaction, where sidewalk shows by musicians, magicians, clowns and comedians can fill an entire afternoon. Museums are notorious for charging no admission at times when people are likely asleep. Phone the museums or visit their webpages to find out the best times to attend.
Some municipal libraries offer free memberships to people renting an apartment in the city.
You now have an opportunity to read books that people have told you about, watch movies from years ago, and listen to compact discs that you would not otherwise buy with your own money. On some days you may not be motivated to leave home, but there are still many productive things that can be accomplished. Write that poem or short story. If you have access to a computer, teach yourself web design and post your creation. Or surf for free stuff on the Internet.