DC really isn't a 24 hour city - there isn't much to do after the bars/clubs close at around 2:30 or so. The only places which would be open are some fast food establishments , convenience stores, and diners. Are you planning to sleep at the airport or are you looking to spend the entire night out and about and just sleep on the plane? The monuments can actually be interesting to see at night - it is a bit of a surreal experience when you are the only one inside the Lincoln or Jefferson memorial and can spend as much time there as you want .

Are there any specific places you are looking to see? Post what plans you have made so far (such as where you will be before 2 am ) and I will try to make some suggestions as far as where to go between 2 and 5 .

Btw, can't think of any 24 - hour restaurants close to the monuments, but there is Prince cafe in Georgetown - 15-20 min walk from Lincoln memorial - that serves decent hookahs and lebanese food. It's open until 4 or so.