Navy Yard's ok, it's just very quiet with not much going on. I live in the SW Waterfront area, which is just across South Capitol St. Safety-wise it's fine, the biggest issue for me would be lack of foot traffic. You could look the SW Waterfront neighborhood, too. I really like it, it's quiet, residential, and pretty safe. There are some problems as you get south of M Street, but otherwise it's fine.
Capitol Hill is a great area. It's got more going on than Navy Yard and SW at the moment. If you live on the SE side you could walk to work or take the Circulator bus from Eastern Market.
For info on the Navy Yard area, you could read http://jdland.com/dc/index.cfm