NYC to ATX Post-Christmas

[MollyATX]

My partner and I are planning a 10-day road trip from NYC to Austin, TX after Christmas 2018. We will fly to NYC and spend the holiday there, then rent a car and take our time driving home. I have done a (cursory) search for suggestions on this route, but have some specific concerns I hope this user group can address:

1) Best place to pick up rental in NYC area? I know city-center and airports tend to be higher-priced, so if anyone has input on where to make a reservation for pick up (most likely a large sedan or small SUV), would be much appreciated.
2) Route choices - I've looked at both an upper (cross the mountains) route and down the east coast and through the gulf states route, and was wondering if the weather during the timeframe (December 26th to January 6th) should play a role in my decision for the route. He's an experienced winter driver, btw.
3) Since New Year's Eve falls within this timeframe, any suggestions on where to stop on the route and enjoy the festivities? Edit: looks like Nashville may be the spot for NYE.
4) And lastly, I would love to either hear feedback from anyone who has done this road trip before, or can point me towards threads in this forum specifically for this route (or close approximation).

Here is the tentative itinerary (w/ approximate drive times):
Day 1: Pick up car in Newark, drive to Atlantic City (3H)
Day 2: AC to DC (3H)
Day 3: DC
Day 4: DC to Bristol, TN (6H)
Day 5: Bristol to Nashville (5H)
Day 6: Nashville
Day 7: Nashville to Memphis (3H)
Day 8: Memphis
Day 9: Memphis to Hot Springs (3H)
Day 10: Hot Springs to Dallas (5H)
Day 11: Dallas to Austin (3H...4, if we stop at Czech Stop, haha)

Thank you all in advance for any advice!

Molly