Ford's Theatre in Washington DC

I recommend Ford's Theatre for families with school age children. It's a great educational destination. Young children probably won't get much out of it, but they are welcome. You can move through the exhibits at your own pace. Ask about the FREE Junior Ranger program for kids ages 5-12 when you arrive. It's a great way to help kids get more out of the exhibits and they will receive a souvenir gold badge at the end.

If you reserve a "free" ticket online, you get assured a reserved entry time but pay a $4 - $10 processing fee per ticket. If the website (ticketmaster.com) says that certain days are unavailable, that just means online. You can still often get same day walk-up tickets for free (20% are available in person I've read). BUT NOTE: this is a timed entry tour, so the walk-up ticket you get at 9 am might be for a 4 pm entry time.