We live in southern most part of NY state and travel I95 to HHI.
Leaving 4 - 5 am it takes us about 14 hours with stops for gas/restrooms/eats. It is 810 miles approx for us.
Leaving NY around 4 -5 am works well for us to avoid Baltimore & DC morning
rush & Richmond's too.
If you're looking for an overnight stop DC area I'm guessing may be around 500 miles for you ? You may want to stay in Alexandria if you'd prefer to avoid staying in Washington DC itself ( you can expect to pay about $40 to valet or regular park you car at DC hotels - hotels outside DC are more likely to have no fee parking ).
We use Priceline to book DC & that area - we bid Resort or 4 star or 3.5 star ( we find below 3.5 star to be too unreliable in quality & upkeep); check out winning bid histories on website bidding for travel.
Rocky Mount, NC is also an overnight stop we prefer - - southbound Exit 138 / Highway 64 East - it is the Rocky Mount exit that has hospital located at it - Winstead Avenue : there is Hampton Inn & Courtyard Marriott among others that are good quality and there is Outback Steakhouse, Highway 64 Diner & Sonic nearby. I believe there's also a nice shopping mall in area although we've never been.
In Florence, SC definitely Magnolia Mall/Convention-Expo Center Exit is best
( I believe it's Radio Drive / David McLeod Blvd, will try to locate my travel notes & post back specifics ETA Magnolia Mall Exit in Florence should be 160B southbound iirc, may be 160A )
- - Hospitality Blvd. off David McLeod has Hilton Garden Inn, Springhill Suites & others; Chili's and others (Ruby Tuesdays) on both side of road where hotels are located & on Magnolia Mall side.