I always try to have a container of fresh water, a nice towel, working jack, and good spare. I used to carry a lot more (spare belts and hoses, small tool box), but last 10 years or so I stay on interstates and have a cell phone, so I don't feel the need.
I figure if it's more than a flat, I call road service, hydrate as needed, and use the towel as a pillow and get quick nap waiting for assistance.
...before the leaving and about 1/2 way - check tire inflation and inspect for bumps and bruises, check fluid levels (oil, trans, coolant, brake) and it never hurts to run by an auto parts store and have them check the charging system.
Have a fun trip!