After an ill-fated morning (which included sending my son to his rescheduled-at-an-inconvenient-time Spanish class only to learn that most of the class was gone so they watched Finding Nemo) we finally made it to DC last week to visit the National Cathedral. It's not free anymore, which is not unreasonable in my mind since it receives no public support but does receive hundreds of thousands of visitors every year. We skipped the guided tour and did our own exploring after paying to enter. I'd downloaded a few tours so it worked nicely.
If you'd rather not pay to go in, there's always no charge on Sundays or if you're going for a service. You can always walk around outside too, if you like.
The building was started in 1907, the first services were held in 1912, and it was finished in 1990. There's plenty of US history here and it really is more a national building rather than a DC one, but I love visiting and wanted to make sure my son went too.