Regarding DC - if you are planning on staying with in proper DC, you don't need a car. Most sights with in DC are accessible by Metro. Parking in DC is expensive, so I don't recommend a car. Depending on what you want to do, here are a few suggestions:
Bookmark the Washington Metro site:
https://wmata.com/ You can plan your itinerary from this site. It's quite useful.
Shopping/Walk around:
1. Visit Georgetown: has many shops, coffee-shops, bookstore, restaurants. Good to visit both during day and late evening (shops are open till 9). 5 - 10 minute walk to closest metro (don't remember the name of the station though.)
2. Adams morgan: has many shops but is mainly known for restaurants and bars. Perfect to visit during night. Has a metro stop. Don't drive here. Parking situation is horrible.
3. Dupont Circle: Shops, restaurant, coffee, bars, etc. Visit day or night. Don't drive. Take metro to Dupont Circle Station. You can walk to nearby neighbourhoods, such as 17th st. which also has shops and restaurants.
4. Chinatown: A small neighborhood but has nice bars and restaurants, especially some nice upscale restaurants. Again, parking is bad so take metro.
Museums (see :
https://www.museumspot.com/cities/dc.htm)
1. Air and Space: This is quite popular with visitors (though it's not my cup of tea.)
2. National Gallery of Art: Awesome. Do go here if you like museums or even if you don't. Love the bldg.
3. Hirshorn museum: Sculpture mueseum.
Monuments:
I really like DC monuments at night. If you follow my advice and want to explore them at night, I highly recommend the following:
1. Lincoln memorial.
2. Roosevelt.
3. National Monument
4. WW memorial.
There are many nice restaurants, which I am assuming you can easily find online but if you want specific recommendations, let me know. Let me know if you have any other specific questions. I have been living in DC for 6 years now.
HTH and enjoy your visit.