In short
The Smithsonian museums — natural history, air and space, American history, African art, the National Gallery — are free, without exception and with no paid ticket. It is the largest free museum complex in the world.
The National Mall lines up the memorials over three kilometres, from the Capitol to the Lincoln Memorial. All of it is walkable.
What it really costs
Housing is expensive, but the culture budget is close to zero: a week of visits can cost nothing beyond transport.
The metro covers the city and the suburbs. It closes relatively early on weekdays, which catches people out.
What nobody tells you
Some sites now require a free but compulsory booking, with slots going weeks ahead — the African American history museum in particular.
The cherry blossom, in late March or early April, draws a considerable crowd and pushes accommodation prices up. The exact date varies each year and is announced a few weeks ahead.
Summer is heavy and humid: the city is built on former marshland and July and August are punishing on foot.