A more scenic route from DC to Savannah, that probably takes an extra 2 hours or so, is:

I-66 west to US 29 south to I-85 south to I-77 south to US 321 south.

This takes you through Charlottesville, Lynchburg, and the Blue Ridge foothills of Virginia; and Greensboro, Charlotte, and Columbia in the Carolinas. The slowest part is US 321 through South Carolina, which is only 2 lanes and goes through many small towns with 30 mph speed limits.

Hotel options on this route are noticeably more upscale than those on 95. Charlotte is a nice stopping point.