Staying in and making dinner is so cheap and it is fun to cook together, have a nice dinner in your own home without all of the extra noise of a restaurant, and then clean up together. Or one person cooks, the other cleans, you both make dessert.
Another cheap date is to go on a scenic drive somewhere at dusk and stop somewhere to lay on the hood. Nothing better than that.
Most thing happening outside are cheap or free. Farmers markets, community movies like the OP mentioned, parks, hiking trails, etc. Even if you have to a pay a small fee to get in a state park it is cheaper than most dates and there are usually plenty of things to do for an entire day in the park.
Volunteer together at a race or somewhere else. You'll be surprised how much fun this can be.
If you are both runners go be a spectator at a high school cross country/track meet. Seeing a bunch of kids who are just beginning to learn is inspiring sometimes.
My boyfriend and I are both in grad school making next to nothing and we still manage to have fun and go on "dates". We don't need to spend a ton of money to be happy with each other.