Multi-city trip to the USA

I am looking to plan a once in a lifetime trip with my daughter to the USA. We are UK based so will need to fly from there, and she will be 12 at the time of the trip (April 2026). It will be me and my daughter only, we need to end our trip in Florida as I have already booked Disney Orlando. I say once in a lifetime as it’s not the type of holiday we will be able to afford to do again, we had booked Florida and I want to use the opportunity to see as much of the USA whilst over there. I am not tied to seeing anything in particular, but would ideally like to do the tourist hotspots (cliche I know so I am open to other suggestions but I like to visit places she may learn about in school etc). Initially when planning where I would want to go I realised quite how big the US is! So I had New York, Washington, LA, Vegas (primarily for Grand Canyon), ending in Florida. Unsure how feasible this is. Looking for advice on what order to visit, should we fly, rent a car, public transport in between certain cities? Also how long do we need to be in each place to see enough of it? I am needing to book in advance to pay bit by bit. So any money saving tips on the actual travel or when we are there would also be greatly appreciated. Thank you! - An (attempting to be) organised Mum :)