I assume given the forum we are on, you are looking for lower-cost ideas.
Museums...doesn't have to be the big, fancy kind (although there are inexpensive ways to do those...look for the free days, etc). But the little ones are much cheaper and, if you go in with the right expectations, lots of fun. Same with nature centers, etc.
Look for the best inexpensive foodstuff (breakfast taco, chocolate-chip cookie etc) in town. Try a new place each time you get out.
Go to high school or college drama, music or sports events. Sometimes the execution is terrible, but sometimes you will be wonderfully surprised by the raw talent on display.
Depending on where you are, sometimes the public library has great programs, usually for free or very little cost.
For an at-home date, try your own mini-film festival. Pick a theme (Best Picture Winners, documentaries, summer blockbusters) and make it an occasion w. excellent snacks, no phones, etc.
Take a class together, especially if it is something not baby-friendly (complicated cooking, etc.)