Been there too. Broken C2 and damaged C1 from 2001 wreck, re-injured last year when I was hit by a car. Still in physical therapy. And I have a chiropractor visit Monday. Some days I can handle up to 50 mile rides. Other days 20 is about all I can handle without a lot of neck pain.
My most comfortable road bike is an older 1980s Centurion Ironman. I've set the handlebar a couple of inches below saddle height, tipped the bar back slightly so the drops aren't quite parallel with the ground, and shifted the brakes/hoods up about 1/2". The combination is much more comfortable, while not looking like a hobo beer bike with flipped up drops. Weighs about 25 lbs. I have 700x25 and would put on 28's if they cleared the chainstays. Keeping the tire pressure a little lower helps, around 80-90 psi rear, 70 psi front.
I can only comfortably handle my early 1990s Trek 5900 for relatively shorter rides, up to 20-30 miles. Beyond that the stretched out position and lower bar causes neck pain. But it fine for shorter rides.
If my budget permitted I'd go for an endurance or touring bike, top of the bar level with saddle height, shorter stem, around 25 lbs or less if possible, and 700x28 or even larger tires.