It's a little too far to walk to the mall, so you'd have to take the metro. But it's a great area for nightlife and restaurants (much better than downtown or the mall area), and it's quite safe.
I've never stayed at any of the hotels in the aread, and I don't know how expensive they are. But here are a few options...
The
Jury's Doyle is right on the Circle, and a block from the metro:
http://washingtondchotels.jurysdoyle.com/jurys_washingtondcThe
Radisson Barcelo Hotel is about two blocks from Dupont Circle:
http://www.washington-dc-hotels-reservation.com/Radisson-Barcelo.htmlThe
Washington Hilton is about four blocks from Dupont Circle. It's giant and kinda charmless. It's often called the "Hinkley Hilton" because it is where Reagan got shot.
http://www.hilton.com/en/hi/hotels/index.jhtml?ctyhocn=DCAWHHH The
Courtyard by Marriott is right across the street from the Washington Hilton.
http://marriott.com/property/propertypage/WASNWAnd here's a nice Bed & Breakfast, which is about a block from the circle:
http://www.dupontatthecircle.com