Student US trip all over US alone

[NefosUK]

Hey guys

I would like to ask for your help, as I am in the planning stage of my trip

Some details before the plan: First time traveling to the US, as I have enough funds for 2 weeks trip, renting cars here and there( more on that later) and hostels mainly for meeting people. I would travel alone, and the plan below is based about what I have heard about US, so I am looking for some help to make sure that at least it is roughly right.

Car Rentals: I am 21, so I can rent only the likes of a Ford Focus class car, and a bit above maybe, but I would be happy with a that big car. As you will see, I will take rounds for a good reason: If I rent a car and take it back, for 4 days it will be like £170 ish including young drivers "You are a lunatic" drivers fee. If I would drop it at a different location,we are looking at £500....

The plan is, I fly from Leeds to Amsterdam, there to Boston and then New York at the end of March, so this is where it begins.
I plan to spend a dayish or less there as I will be back there at the end of the trip again.
From New York, I would take the train, go to Washington DC, White House etc.
I would rent a car (Ford Focus class from Hertz, I am 21) and go to Toronto ( I know a long drive), spend a day or two there with my friend, then drive to Chicago, with a break in Detroit. I would like to check Chicago out more than Detroit, although if Detroit is interesting then let me know.
From Chicago I would go to Colombus, stay there for a night, go through Pittsburgh, then back to Washington. Drop the car, get on a plane, fly to Las Vegas. Rent a car there as well, go to Grand Canyon, Death Valley, then go to Fresno or Bakersfield to sleep ( maybe stay a night in Las Vegas between Grand Canyon and Death Valley). Check Yosemite, go to San Francisco. A night there, then drive down to LA. Spend a few days there as well, then go do Las Vegas.

And now this is a question here, as It would be a good thing I think. Go to Miami/Orlando, drive around there for 2-3 days, go to beaches, have fun. Then I fly back to New York and have there

The plan is vague and for many reasons. First, this is my rough plan.
Secondly, I do not want to over plan it. So I would like to pin point out the things where I should go, then get the plane tickets in the US flexible so I can change it if I would like to, as for example I enjoy Miami that much that I would like to stay there for more days, then take away few days from New York.

This drip would be easy to do in 14 days, Miami might be a bit of a stretch.
What do you think, is it a good plan to begin with? Would you change a lot on it?