With kids:
Dallas area-zoo, world aquarium, Perot Museum, Heard Animal Sanctuary (outside of Dallas)
Fort Worth area-zoo, museum of science and history, Log Cabin Village, Frontiers of Flight museum, grapevine railroad (ride a traditional train), Grapevine Mills (cosmic mini golf, ice skating, carousel, Sea Life Aquarium, Legoland, movies, restaurants)
Without kids:
Dallas Area- Dallas Museum of Art, game or concert at American Airlines Center or Winspear Opera House
Fort Worth area- Billy Bob's Texas (huge honky tonk), Sundance Square, game or tour at AT&T stadium (Cowboys) or Globe Life Park (Rangers)
You will need a car, public transport won't get you far and things are far apart.