We did Cape Cod to southern NJ on a Sunday via I-95 to I-287 to the Tappan Zee, GSP and I-95 again. Traffic was reasonable (Novermber). Stopped at Timberlane in Clarksboro NJ. The next day we went across the Delaware Mem. Bridge and took 301 south. For Virginia Beach, I'd do Rt 13 down the DelMarVa and take the CBBT.
If you're not doing this on a Sunday, I suggest taking I-95 through Providence into CT and picking up Rt 9 to Middletown, cutting across to pick up I-691 to I-84 to I-684, then as above. This looks like a lot of out-of-your-way, but believe me, avoiding I-95 through southern CT and NYC is well worth it. They've been doing construction in New Haven for 20 years.