Bad weather is the perfect weather for a family trip to the local museum. It is indoors, climate controlled and educational. And, it is not all looking and not touching. Most museums have an interactive area where kids (and even teens) can have a hands-on experience.
You may be surprised by the number of museums in your area when you do a web search. For example, in Nashville you can visit the Frist Center for the Visual Arts (with fancy paintings and traveling exhibits), the Country Music Hall of Fame and Museum, Lane Motor Museum, Andrew Jackson’s Hermitage plantation, Tennessee State Museum, Musicians Hall of Fame and Museum, Adventure Science Center, Tennessee Sports Hall of Fame, the Military Branch Museum, Tennessee Central Railway Museum. Almost every community (or community within driving distance) has small or large, formal or quirky museums. All you have to do is look for them.