A tour of the Fort would likely be the most interesting, and could turn out to be pretty cool if you're into seeing Army hardware up close and personal (depending on what your kids are able to show you).
Most likely the weather will be cold, but roads will be clear. If it does snow, then just stay in where you are for a day, and the road departments will clear the roads.
West of Ft. Riley is Abilene, Eisenhower Museum, Old Town and such. Ft Riley itself has museums. East of Ft. Riley is Manhattan and Kansas State University. Most things to do in that area will be museums or historical sites and events unless K-State happens to be putting on a musical or some such event.
I grew up in that area, it is rich in culture, but a long way from Broadway.