Touring - Help me plan my route :)

Here is the thing, I am moving to California from New York and I am driving my car cross country. I know this is a bike touring forum, but I am a fellow cyclist and I have no clue where else to turn.
The starting point is NYC and the destination is San Clemente (by San Diego)
I would like to stick to faster moving highways and roads but still see some of the beautiful country.
I am not in a rush to get to west coast, but I do have very very limited funds and would like to spend the least i possibly can.
I am bringing a tent with me and would enjoy stopping places and camping out. The problem is I am very new to this Country and not well informed about the nice places that this country has to offer.
I really enjoy national parks and open lands with beautiful landscapes and absolutely adore nature.
Because I am going to be stationed in California, I would like to skip stopping in neighbouring states of Arizona, Nevada and Oregon because I will most likely be making frequent trips and seeing the west coast.
I have heard great things about Colorado and would love to spend some time there.
If you can help in any way planning my trip I would really appreciate it.

1. Point your car southwest, continue to bear southwest gradually. :D

2. Go to your local AAA (American Automobile Association) and ask for a set of US maps - state maps and one general US map, and a set of campground guides for the states you'll be going through.

3. Have a good look at the general US map and decide if there are places you'd like to see. You may need to return to the AAA and collect more information.

4. As you drive on the faster moving highways, take the time to stop at some of the rest stops they've got every so often along the way. Pick up more maps, compare maps, select the roads you like. These places may also have brochures on parks, campgrounds etc.

5. If you spot a tourist information centre in a town you're driving through, stop and collect more brochures etc. for the stuff you're interested in.

Colorado and Utah are states that you need to drive through. When in CO drive up Pikes Peak or hike it[more fun] near Colorado Springs. Remember all the big Nat'l parks like Arches and Zion and RMNP and so on. Maybe Death Valley, CA too if your car doesn't overheat easily. Have fun!

Thanks you for your suggestions. I forgot to mention that I will be taking 3 bikes with me on my roof rack that will be steal proof(I hope). Anyway one is mountain bike and one road bike. The other is my girlfriends, so I can do some riding along the way too.
Pikes Peak and Colorado Springs look like a must visit.
Thank you :)