You don't need gloves in May, but you may need an umbrella and a light jacket. You've got to see The Spy Museum, it's terrific! They teach you how to spy, and then they teach the history of spying. Really enjoyable.
For restaurants, go to Adams Morgan, which is near downtown and a short walk from the Metro. I like Fasika's for ethiopian food, which is delicious. There's also a restaurant for food from Ghana and there's The Diner for American food. They're all reasonable and right next to each other on 18th Street. If you want to go to 13th and U, which has a lot of clubs, you should try Ben's Chili Bowl. They're known for the hot dogs, but their chili cheeseburger is outstanding. You can always get cheap meals at hot dog carts, too, and I consider the hot dogs second only to Chicago and better than New York.
Don't rent a car, take the metro. Reagan airport has a metro stop, and most places downtown have one, too. It's not expensive and it's very clean.