Just do it, as one tends to say.

The USA is designed around road vehicles and cars in particular.

3 1/2 weeks won't be enough for what you want to do, but that's your problem.
I have spent a total of about 8 weeks in the state of Florida alone over the past 30+ years; for instance you won't get around all of the FLA places that you mention in your time frame and drive across the route you want.

As another instance, if Disney World has to be done then so be it, but what about Sea World or Cape Canaveral (was named Cape Kennedy for a while)?
They are all designed to relieve you of the contents of your wallet.

Incidentally, one time I was there I also had to have a convertible; I can't remember which one but the hire car was chopped in for a ragtop; then it was necessary to drive it along Daytona beach.
From that, I learnt that there was/is a 10 MPH speed limit on that beach.

Second memory: It was in Florida that I saw my first "chain gang"; all out there cutting the grass in the mid-day sun.
A Cool Hand Luke likeness.
That was about 20 years ago, so maybe they don't do that any more in Florida state?

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Dave

3 months is sufficient. First of all, let me wish you a great journey ahead. I would suggest you that you should carry a road map with you whichever country you visit, It helps you save your time and effort to visit a particular place. Also, I would like to recommend watching some travel videos to understand the people, places, and culture better. In this way you will enjoy the vacation and will cherish the moment to the fullest.

Sounds like a good trip to me. yeah, 3 months might seem like not enough time to some people, but American's so that trip (and back) in 2 weeks vacations, so there isn't any reason you can't do it.

Your food budget might be low - it's possible to spend a lot of money on food here. Again, doable if that's your budget but (especially if you want to eat out from time to time) expect to handle some of your cooking. In the SE, look for the BBQ pork and sweet tea. Texas is Brisket, further west is fry bread, In Florida (more likely Southern LA) try some fried gator. I'm liking the fried gator lately. Always, always look for small local places rather than chains.

If you can, get a National Parks Pass. They aren't cheap, but if you are looking to hit more than a couple they are totally worth it. Be aware they are good for entrance fees only - tours, parking, all that other stuff is extra. I found this particularly annoying at Mt Rushmore - which is technically free but they charge for parking.

I like AirBnB, but have limited experience.

It's hard to make real suggestions on what to see, without knowing what sort of stuff you like seeing. Just about everything is available along the way, from the weird to natural and man-made wonders - a fair amount of history too. Lots of little towns and ghost towns and big cities. This is where the 3 months will seem like not enough - you really don't ever run out of stuff. But that's not a reason to not go.

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I write books about motorcycle travel. Small, cheap, motorcycle travel. Also superheroes.

I'm right in the middle of a trip like you're planning - we've done about 5000 miles so far with about the same again to go. I'm writing this from a hotel in Vegas (yes I know!) and we're heading off to Los Angeles tomorrow. I'm happy to give you any advice / help I can but you asked a lot of questions and it'll take forever to tap out a comprehensive reply on my IPad. I'll try to do bits as and when I get the chance but in general there's nothing in your plans that couldn't work.

First bit of advice - don't underestimate how big the U.S. is. Orlando to L.A. via the Grand Canyon and other photogenic stuff in the area is a really long way. With your time scale you'll be driving past stuff you really want to spend time at. Some US friends I showed your post to gave the "Irish" response - if I was him I wouldn't start from there, but I know how much of a non negotiable item something like Disney or Universal can be from our previous US trip. This time we had Graceland as the "don't argue" destination (and it was really good!).

1. Not enough time for that distance if you want to see anything very much rather than drive 8 hours per day every day.

2. Consider using car delivery companies like (?) Driveway - you pay for gas, they get the car delivered. Could probably find one from Miami to LA. It'll save you 700 quid....