I'd recommend a hotel in Pentagon City or Crystal City in VA. You can take the Metro into DC and you'll probably get a nicer hotel for a better price. Also, there's a nice mall at Pentagon City if you are looking for some shopping or some cheap food at a food court.
As a rule, avoid/be cautious of hotels in the northeast or southeast quarters of DC.
Dupont Circle is a nice area, but it can be expensive and it's more of a 20/30-something party area of town, so if you are going with family or bringing your kids it would not be an ideal location. Staying in Dupont Circle you'll also be close to the metro (and you'll get to see one of the longest underground escalators - total vertigo feeling). A hotel downtown would put you closest to all the typical tourist attractions (Nat'l Mall, Smithsonian Museums, etc.).
Capitol Hill is an okay area, but you need to keep an eye on how far away from the mall you will be. As you get further east of the Capitol, the neighborhood is less tourist friendly. If you do end up near Capitol Hill on a weekend, go visit Eastern Market - an indoor/outdoor farmer's market. It's a local favorite and will give you a real sense of the local culture and restaurants. There are also great restaurants around Eastern Market that are unique to DC.