I just wanted to make sure you know, since you said that you want to avoid pork and wine, that many of the restaurants you've mentioned are not necessarily going to serve halal meat, if that is a concern. Some desserts may be made with alcohol, as well. You may wish to call ahead and check if this is important to you.

For food, you could try NuVegan Cafe. They serve vegan soul food and, since they are all-vegan, there is no concern about pork and everything should be halal. Plus, the food is delicious.

I don't know which museums you are planning to visit, but I highly recommend the Smithsonian American Art Museum. It is a few blocks away from the National Mall and the majority of the museums but it is a wonderful museum with many gorgeous and fascinating pieces.

If you are going to the Museum of the American Indian, they have a great cafe downstairs that serves Indigenous foods from all over the Americas.

Since I saw you mention in another comment that you will be visiting in mid-October, I do recommend bringing jackets and clothes for cooler weather, wind, and rain, as well as clothes you would be comfortable in if the weather is moderate (24 degrees C or a little warmer isn't unheard of at this time of year).

I hope you have a wonderful trip!