I have attended Nationals game in DC. Seats behind first base are in sun, and people roast there and have to wear sunglasses. Behind third is better.
"Teaism" is a nice local (not chain) place to stop for a tea/food. Hard to describe - you can get a very tasty chicken curry - or a bento box - and bubble tea - other things like that - and they are located near the Archives where you can view the Declaration of Independence and the Constitution if you are into old documents.
If you are around in Dupont Circle, try - La Tomato for nice light Italian - I used to wait tables there in my 20s - so I can vouch for it.
The Childe Harold - also in Dupont Circle - if they still have the Wild Billy Burger on the menu - used to love that - a steak filet on an English muffin with bernaise sauce. Plus, their other burgers are good.
Pizza Paradiso - also near Dupont Circle - locally owned (not chain) wood oven pizza with lovely fresh ingredients.
For the NYC part of the trip - if you are staying in Brooklyn - you can do Coney Island and the beach in one ... because CI is on the beach. There, I recommend Fulton street for shopping for sneakers and Juniors for authentic Brooklynese food. www.juniorscheesecake.com/
Manhattan, I like the Cast Iron district. Pretty and quiet. The tenement museum is nearby, and I definitely recommend that. It is in a 6 storey building that, believe it or not was shuttered up since the 1940s - it was a tenement for immigrants - and when they investigated it - they found layers after layers of stories of immigrants that lived there. You get to feel how difficult their lives were - no elevators, no indoor plumbing, no AC, coal stoves to cook and heat. OK for those on the first or second floor maybe - but the 6th!? www.tenement.org/
However, if you like the show Cake Boss - you can take a ferry over to Hoboken, NJ, and see NYC from a whole new perspective, and pick up some "lobster tails" which are actually a pastry.
Have fun!