There was a period where my boyfriend was underemployed due to a lay-off. For months we had practically no budget to do things - but things we did.

We made picnics and visited the parks.
We went for walks in green spaces and along the river.
We went to the art gallery (free or by donation) each week and participated in free art classes.
We went to the museum for a cheap coffee and walk about (I volunteered and could get us in for free)
We stayed in and played cards.
We prepared meals together.
We contacted friends and went for coffee.
We paid attention to the local events calendar and were frequently attending free events like Fringe Festivals and concerts (and when they weren't free we volunteered together)

These things cost little or no money. There, if you do only one of these things a week, I've just given you two full months of activities.