As a fellow foodie...I have a few suggestions.
My favorite hangout is Kramer's Books & Afterwords. Located at the t It is a bookstore with a restaurant in the back. Interesting wine list, upscale-but not too pricy food. Be sure to save room for dessert--outstanding pie.
Be sure to save time to peruse the bookstore. You will find an eclectic mix of books that you won't find in a typical bookstore.
Take the Metro to DuPont Circle (red line), take Q Stree exit, and you will see the sign after you get off the escalator. And Metro is super easy, and cheap, in my opinion. Uber is great, but traffic is not...
I'm big fan of Asian food, so I always spend time in ChinaTown. My favorite place there is Royal Thai. Fantastic, authentic Thai cuisine. Order Green Curry Pad Thai. You will thank me later.
If you are a bit adventurous, try Chinatown Express. Understand that there are whole ducks in the window, and a fish tank where the catch of the day is swimming. No atmosphere. But OMG the food is amazing. Steamed dumplings, hot and sour soup that is actually hot AND sour, lobster lo mein....yum!