We actually find a great deal of free or relatively cheap entertainment. Museums were mentioned above. I'd like to add galleries, festivals, and community events to the list. Many are free of charge or by donation. I say check your local free weekly newspaper as this is the most likely place to learn about coming up events in your locale. Another fabulous source of what's happening in your community is the Eventbrite website. It is gaining popularity and your city might be included.

We make dinner together when we can.
We play cards and board games.
We avoid using phones and other devices when in one another's presence (if it is absolutely important enough the person will phone you).

If you DO have some room in your budget for entertainment, perhaps try an art class together. Paint nights are good fun.

Discover your the community you live in and think outside of your usual 'box'. Pretend you are a tourist.