Take a day or weekend trip to a lake or ocean. Bring along a fishing pole or just a book and a picnic basket. Enjoy the quiet completely by shutting off your cell phone so that you are without distraction. If you are taking a weekend trip, pick a spot that has free or cheap camping. Relax with your entire family in the outdoors for days with little money. Plan activities such as grilling, hiking, storytelling and swimming.
Take a day or two to visit popular landmarks within your state to brush up on your state's history. You will likely also encounter a variety of attractions such as diners and museums that you didn't originally know about. Document what you discover with a journal and pictures. Create an album of your pictures and thoughts to commemorate your landmark trip.
Many states have smaller or medium sized theme parks. Lesser known theme parks are generally less expensive than the theme park giants such as Disney World or Universal Studios. Make the trip an event with your partner or family. To save money, pack a lunch and keep it in a cooler in the car so that when you get hungry you can enjoy a filling lunch without emptying your wallet. Many parks allow re-entry if it's within the day; ask for a bracelet or stamp before you exit.
Visit a state park in your area for one day or an overnight stay. Many state parks have free day passes though some charge for overnight camping. Plan a hiking trip to enjoy the fruits of nature. Identify flowers, plants or animals that you encounter. Record this information in a journal or take pictures to document your findings. Use your hike as an excuse to hunt for the perfect campsite. Make yourself a weekend home in the woods with a hammock, tent and fire pit, provided that the park permits camp fires.