Thank you for all the suggestions of things to see in DC. I'm excited to try them all out. Amy suggested I ask her brother for ideas, so I did, and boy howdy, the man is thorough. I want something like this for every city I will ever visit. I am posting it for all to reference for future trips to our nation's capital. Thank you, Pepper!
I've been a lot of places in the world, and Washington is my favorite city. It seems to have everything. I'll give you some suggestions based on my lifestyle and my interests. Let me know if you have specific questions about anything I leave off the list, or if you have a specific set of interests/hobbies you would like to cater to.
I think the number one thing to do in Washington DC is attend oral arguments at the Supreme Court. It is a great experience for anyone - no matter the age, education level, or personal interest in constitutional law of the attendee. Unfortunately, oral arguments will not be in session in June; I only mention it so you will keep it in your back pocket for the next trip.
Looks like you are getting into town on a Friday. Is it a late arrival? My favorite thing to do on Fridays during the summer is a picnic at the Sculpture Garden. They do free jazz concerts every Friday evening - I think from 5 until 8. (The great thing about DC is that nearly everything is free) You can get food at the little cafe inside the garden (my favorite is the spinach & artichoke bread bowl - but the best thing is to bring your own food, lay out a blanket on the grass, and sit/lay down listening to music and relaxing. Wine & cheese is a popular item for other families/picnics. Obviously substitute your drink of choice, but there is a really good cheese creamery (Cowgirl Creamery) just a few blocks from the Garden. I'll give you the specifics at your request. The garden has some great art, the centerpiece is a large fountain to sit around, but the music and atmosphere is fun. It's a great place to spend some time before seeing the monuments.
Go see the monuments at night. The sculpture garden is right on the mall so you can take a nice walk after the jazz concert. Go see the Washington monument, the Lincoln Memorial, and the Jefferson Memorial. Friday night would be perfect - it's a fitting introduction to the city. Also see the war memorials (Vietnam and WWII).
What to do on Saturday? For breakfast, try going to the Eastern Market. There is a place at the indoor market called Market Lunch that is deservedly famous for its blueberry buckwheats. Come back to the mall area and go to the Art Museum. I think the east wing is better, but you will be able to see both. The reason I suggest this museum on Saturday is because the crowds will be large at most other "popular" museums. The African American Art Museum is another interesting place to go that will not have many crowds. You can venture over to the Building Museum and maybe the Police Memorial as well. Those are near judiciary square, and you could eat dinner in Penn Quarter or China Town. Matchbox is a great little restaurant for a burger/sandwich. Ella's Woodfired Pizza is another good place close by. In China Town, my favorite place is Tony Chen's - you can't miss the big front on H Street (try the honey walnut shrimp if you go). Other great restaurants to try in the area are Rosa Mexicana (just for the fresh guacamole) and Jaleo's (Spanish tapas). Jaleo's is very well known and very popular - I'd actually recommend not missing it if you like tapas. It is on the SW corner of the Verizon Center. I know Saturday is sort of jumbled, but I would focus on places that are not too crowded. Another great place might be the Library of Congress. This is the best building to see inside - better than the Capitol Rotunda - but few people go inside to look around. It is a "can't miss" on your trip.
Sunday brunch is the best meal of the week. Unquestionably, the best place in DC for Sunday brunch is the Kennedy Center. You will need reservations in advance, and it is relatively expensive, but it is a great experience. Enjoy the views and the food, and definitely take a look around the Kennedy Center when you are done. Other peaceful places to go on Sunday are the National Cathedral, the National Arboretum, or Roosevelt Island. Let me know if you would like help deciding between any of them.
Monday is the day you should try and get to your "can't miss" museums. I recommend the Holocaust Museum - sobering, but unforgettable and well worth the time. You will need to show up earlier and get "passes" for a later time. They only accommodate a certain amount of visitors each day, and the passes are handed out in the morning for each day. Walking around Georgetown is a fun thing to do as well - just to see the shops and restaurants. Maybe you could do that in the afternoon before meeting Steve in Adam's Morgan for dinner. I prefer Adam's Morgan to Georgetown. It has a very European feel and a good social crowd for our age. You can walk across the bridge from the Woodley Park metro stop and just walk down the sidewalks looking for a good place to eat. There will be patio seating everywhere with menus posted on the sidewalk - lots of different ethnic restaurants. One of my favorites is Meskerem - an Ethiopian restaurant. Remember that dinner time there is about 8:30 or 9:00 so don't get there too early.
Tuesday I would go to the zoo. you are staying right by it (the zoo is free as well). Go see the Pandas. A good place to grab lunch might be Ben's Chili Bowl on the U Street Corridor - lots of history and probably a "can't miss" eating experience. In the afternoon, head over to Arlington National Cemetery. This is also a "can't miss" spot. Go to the Kennedy graves, the Lee House, and the changing of the guard ceremony. The ceremony is another very sacred experience, perhaps rivaled only by the Lincoln Memorial. The Lee House has really interesting history and offers one of the best views of DC. Have Steve meet you over at the Iwo Jima Memorial Tuesday night. It is also a "can't miss," but Tuesday night during the summer is the best time to go because the Marine Corp Band performs a concert from 7:00 until 8:00. Stop by Dupont Circle on your way back to walk around. I recommend a little french bistro there called Bistrot du Coin for dinner. It is one of my favorite little places to eat - and the foie gras is really good.
Here are my rankings for the places I mentioned - as well as things I didn't mention.
Best Restaurants (this is a tough one so I will break it into other categories)
White Tablecloth (more expensive obviously):
2941 Restaurant (Falls Church, VA)
Vidalia (Dupont area)
Blue Duck Tavern
Mid-range (I suppose I could also call this ethnic)
Jaleo's (Penn Quarter - Spanish tapas)
Zaytinya (Penn Quarter - Greek tapas)
Tony Chen's (best in China Town)
Kamlaya (best Thai - also in China Town)
Meskerem (best Ethiopian - Adams Morgan)
Bistrot du Coin (best French - Dupont Circle)
Ben's Chili Bowl (U Street Corridor)
Matchbox (China Town - pizza/sandwiches)
Ella's (Penn Quarter - pizza)
Clyde's (Verizon Center or Georgetown - American)
Best Smithsonian Museum:
Art (East and West)
National Portrait Gallery
Tomb of Unknown Soldier (changing of guard/Arlington)
Best Thing Most People Miss:
Supreme Court (oral arguments)
Library of Congress