The NIH is unable to provide housing for summer interns. We can offer some information that may help you in finding a place to live. However, any information we provide is just that; it does not constitute advice, nor are we endorsing or approving any companies or services.
Many different hotels and apartments are close to NIH, on an NIH shuttle route, or within walking distance of metro stations, see NIH Clinical Center Visitor website: Hotels and Motels. Previous DSRTP students have stayed at the Monterey Apartment, see NIH CC list for information.
The Moving Guide (PDF, 518 KB)  prepared by the NIH Office of Intramural Training & Education, provides additional suggests for temporary/short term housing.