C.O.
Where are you staying?
There are a ton of things to do in DC - there is the International Spy Museum (not free but you can do a Spy Ring game), Smithsonian Air & Space, Natural History..the National Mall - just sit and eat lunch and watch people....the National Mall has vendors and SMALL outdoor food vendors, but none of them cater to vegetarians.
Your white house tour - you need to let them know it's medically necessary. I will assume you already have your tickets.
Things like snacks are usually OKAY as long as they are NOT CONSUMED or OPENED in the facilities...
Almost any thing you want to do is easily accessible via the Metro. I would purchase a $20 metro pass for each member of the family so that you can just GO instead of waiting on a bus or a cab.
It will be VERY hot and HUMID here in July. It's already VERY hot - we've been in the 90's with 80% humidity for the last week - VERY unusual for us.
Dress comfortably. Tennis/walking shoes. hats, sunscreen, etc. your backpack will be searched when you go into the museums - they will most likely tell you that you cannot open the items IN the facility. The Air & Space museum has a McDonald's food court.
You can also do the Capitol Building. Check to see if they will be in session and see if you can sit in on a debate - that's always fun!!! :)
I live in Reston, we are 22 west of DC and my husband takes the bus and metro in EVERY day...in Rosslyn/Arlington (Ft. Meyer Dr) is a metro stop and the Newsuem - a museum for the News Media - which can be interesting as well.
I HIGHLY recommend the Vietnam War Memorial as well as the other memorials on the National Mall. The Tidewater and the Lincoln Memorial are nice too...July is too late for the Cherry Blossoms - which is just WOW!!! Do that in March/April...that is just amazing to see the trees - it's just WOW!!!
Please inbox me and let me know where you are staying...I'll do some more searching for you!