The cheapest US city, many world class free museums and free sights means that you only spend money on food and accommodation. The only thing that limits the time here is the amount of museums you can see day after day! The city is easy to get around, a bike or walking will do it all. The nightlife can be hit and miss here.
Insider Tip:Smithsonian Museums are great! The Air and Space and Natural History museums were my favourite. If your time is tight in DC get a bike.