From SF to NY in three months

[Arikael]

Hi

I'm a 30 year old male from switzerland and got a taste of the US in august 2013 when I roadtripped for three weeks (San Francisco, Grand Canyon, Las Vegas, Death Valley, Yosemite) and approx. 2000 miles.

Now I want to fulfill a dream of mine by traveling from San Francisco to New York starting from mid of may 2015 or begin of june to august.
I have three months for this adventure.
After some research here and in other places I came up with the first draft of my journey
https://roadtrippers.com/trips/usa/5764394


How I plan to travel
The things on my map are not all must-see they are more waypoints so I see where I go and how far it is.
I first thought that I will include Yellowstone National Park, but after some thinking it's seems a bit too much to drive (bear in mind I'm from tiny switzerland ;) )
The last time I drove 2000 miles in three weeks which was cool but my personal top limit of driving, so I will probably spend more days on less destinations. Maybe this will change, maybe not.
Normally I only book the hotels at the beginning and the end of the trip. Everything between I book one day or so in advance. Worked great last time, even in august.
On my travels I'm really interested in nature, history and music and I normally don't spend too much time in big cities because I usually get bored after some days ;)

I have the following questions regarding travelling:
What places could you recommend in colorado? I'm interested in kajaking or river rafting and hiking.

Like I said I want to start mid may or begin of june. I know Tioga will probably be closed then and it can be quite cold.
As far as I know river rafting (Colorado River for example) should be possible then, correct?
I know I will arrive in august on the east coast (probably high season too). But I assume SF to NY is better than NY to SF considering the months I'll travel.

I plan on staying in motels and from time to time camping.

If you have other tips what I absolutely have to see, tell me :)

Costs
It will probably be expensive because of the one way trip with the rental car (don't want to buy a car, too much hassle)
I don't want to spend more than 30000$ including car, flight, and probably the rent I still have to pay for my appartment at home. Those three things will probably cost already 10000$ but I think I can get along with less than 30000.