Look through your newspaper and you'll likely find a lot of free/inexpensive underground events going on. Some of my favorites are...
Coffee houses: fun and relaxing, a lot of them host poetry/storytelling nights and feature underground bands and music groups (African drums, anyone?)
Outdoor Cinemas: Fun in the summer! If your city doesn't have one of these, borrow a projector and watch a movie on the side of your house. While you're waiting for it to get dark enough outside, enjoy a barbecue, make kabobs, etc.
Ride the city bus and people watch.
Go horseback riding.
Go to the humane society and play with the animals.
Finger paint.
Cook/bake something together. Endless opportunities to kiss frosting off each other's noses.
If you're artsy, go to a free art gallery/showing. Or try one of those paint-your-own-pottery places. Experiment with paper mache.
Go hiking. Bring lunch.
Get together with friends have a Food Fear Factor contest. Create rounds of progressively gross/weird food. (ex. safer foods are typically spam, soda w/ aspirin, or toothpaste mixed with water. For more daring options, find an asian grocery store and cook chicken hearts, pig snout/stomach, or bitter melon juice). A delicious prize is a must.
Go watch a little league game together. If you like kids, marvel over how cute they are. If you don't, make fun of their blunders.
Do yardwork/gardening together. Sounds boring, but it's hands-on, calming, and the silence is golden.
Go to a used book store and compete to find the worst book cover, title, etc. Fantasy and romance novels are typically winners.
If you live in a college town, check out what events are happening at the college. Usually a play, music performance, or film is showing for a low or nonexistant price.