US-1 does run the entire length of Florida, but it's kind of weird to start, coming through Georgia (Folkston) as 301 or 15, then turning into 23 or Rte1 or 15 at Callahan. And then it becomes Philips Highway after it cuts through Jacksonville. Also in Jacksonville is Alt1 (MLK Expressway and Hart Bridge), though I'm not sure where it hooks back up with US-1 south of the river. Since Hwy 1 follows New Kings road for a time, the route from Florida to Georgia probably follows generally the Kings Road that was built in the late 1700s that was supposed to diagonal from Macon through Cowford (Jacksonville) and down to St. Augustine and eventually New Smyrna. I believe the Old Dixie Highway is also part of this route. Anyhow, after Jacksonville when it veers towards the northwest, US-1 is a main thoroughfare that goes north-south along the Atlantic coast of Florida, staying west of the Intracoastal Waterway.
A1A is the road that goes up and down the coast that generally stays east of the Intracoastal. It's often the road next to the oceanfront properties. You can drive it right past Mar-a-Lago or the Kennedy Space Center. But A1A does get cut off by some inlets along the way from Amelia Island down to Miami, including the St. Johns River here in Jax, meaning you have to cross the Intracoastal and often use US-1 in order to pick A1A back up again. Therefore, a trip along the A1A along the entire Atlantic coast of Florida would be mind-numbingly long. If you could get lucky and average 35mph along the way, it would still be over 10 hours from Miami up to Fernandina Beach.
When you want to speed through Florida, then the I-95 is your road. Generally, it's further from the coast than the A1A or US-1. Around Miami, you also get the turnpike and I-75 going north-south alongside the 95. It's a dangerous road, and I think it's used by a lot of drug mules and people escaping from other states, but it's fast. Jax to Miami in about 5 hours.