The kids and you will love the Air and Space, Natural History, National History, go up in the washington monument. Go vist the the Viet Nam Memorial, WWII memorial, Lincon memorial. there is so much to do it is hard to pack it in to one day. I can spend 1 day just in a single musem. Then find a Five Guys and get burgers and fries that are to DIE for.
With the kids the 2 I would recommend most are the American History and The Air and Space museums. The Air and Space is great for anyone interested in aviation (obviously) and has interesting things like The "Spirit of ST. Luis" and the Wright Brothers, but I have found that some people are not as interested in that stuff. The American History has something for everyone! The only issue is as "mrmurdoc34" said, it is hard to squeeze things into one day. I would suggest checking the times some close before others so you can plan them out in an order and see the monuments before or after they close.
Don't worry about crime, everyone scares people with that but as long as you're on the mall and people are around there isn't much to worry about. Just be aware you are in a city.
If they are REALLY little (young) and would be more entertained by a park than a museum, then the National Mall would be good - the monuments can be entertaining for you while they can just play until their hearts are content.
Ditto Air & Space and Natural History (dinosaurs!). I just want to add that in the bottom level of the American History museum is the "Spark Lab" - a cool hands-on science area for kids. Plenty of educational toys and a long bar for the kids to sit at and participate in science experiments led by volunteers.
For toddlers to 5yo, I recommend the National Zoo (for obvious reasons) and the National Building Museum - which has a great play room Building Zone