Weather could be in 50s, 60s, or 70s. Could be sunny, could be raining. Definitely bring layers and umbrellas/rain coats.

National Childrens Museum (not free but fun), Air and Space Museum, Natural History Museum, Library or Congress, US Capitol Tour (get free timed tickets online), National Cathedral, Kennedy Center has family concerts/events I would check out their calendar, Botanical Gardens, walk around the Arboretum.

Since you’ll be here in October it might be fun to go to a farm outside of the city and do some fall activities - hay ride, corn maze, pumpkin picking, apple picking. Washingtonian website has good recommendations.

For food I would use the yelp app to find recommendations close to where you will be staying/visiting during the day. I would recommend getting some seafood, southern food, tacos, sub sandwiches, bbq (although this can be pork heavy, places will have beef and chicken options), and pizza!

Have fun!