The drive is a consistent 3.5 to Norfolk, so probably 4 to VaBeach. Mostly back roads with very little traffic once you cross the York River.
There are two main options:
1. 64 to 295 (around Richmond) to 95 north, take exit 104 (at Petro Sign), merge onto 301, right on 234, take 246 shortcut to 235 and sail into Pax. This route adds 15 miles, but you take advantage of 65 mph speed limit for 125 miles and avoid all the stoplights on route 17. If you add 9 mph to speed limit, this route can be run in 3.1-3.2 hours from Little Neck. If you like Starbucks or variety of view, see below (most of this trip is endless views of pine trees ad nauseum).
2. 64 to 17 to 301 (at Port Royal) and same route thereon as above. Route is shorter, but you have to transverse many lights between 64 and Tappahannock so this route can easily go from 3.5 to 4 hours depending on how the traffic light gods favor you.
I use both routes and mix them up typically using first one on the way up and relaxing on second one upon return.
Note: biggest hassle can be backups at Hampton Roads Bridge Tunnel so make every attempt to avoid the peak traffic there as it can add 30-45 minutes to your trip and a disabled auto in tunnel can really turn into a major delay (spoken from experience). Only traffic in and around Pax is 10K+ people trying to escape the base at COB and play NASCAR on 235. Leave early or late and avoid Gate 1 if possible (Gate 3 and direct to 234 is gouge but it closes at 1800)