Welcome to Travelblog!
It sounds like you have a great plan outlined. Where will you be starting your trip from? Will this be your first trip to the United States? September is a great time to make this trip. How much time do you have for your travels from San Francisco to New York?
Train travel in the United States may not be the best option for you. It is not that inexpensive and the routes will not take you to all of the places you are going. I'd suggest taking a bus or purchasing an inexpensive car for your travels.
$50 for a hotel is going to be as cheap as it comes. In the larger cities like San Francisco you will be able to book a hostel for about $30.
You are planning to go to a lot of places so a car might be your best option.
LA to Las Vegas = 4 /12 hour drive
LA to San Francisco = 7 hour drive there are some wonderful places to visit along the way
San Francisco to Seattle = 15 hour drive
Las Vegas to Phoenix = 5 1/2 hour drive
Phoenix to the Grand Canyon = 10 hour drive
LA to Chicago = 4 hour flight and will cost about $380 per person
San Francisco to Seattle = 2 hour flight and will cost $250
Seattle to Las Vegas = 2 1/2 hour flight and will cost about $275 per person
If you want to do an internet search on inexpensive hotels look at Super 8 or Motel 6.
You mentioned that you want to go to Yosemite NP so I assume you like the outdoors. You may want to explore the Seattle area.
Mt. Rainier and Mt. St. Helens are worth the trip north. My favorite park is Glacier National Park in Montana. I could spend the next hour talking with you about the fantastic National Parks that we have.
Others to consider- Yellowstone National Park, White Sands,
Tell me again how much time you have?
Your limitations are going to be money......and time.
Things to see in Seattle
Pike's Place Market is wonderful. It is down on the water. Just lovely.
Th Underground Tour is very nice. It takes about 1 1/2 hours. It is a humorous tour. Years ago the city was destroyed so they built the new city on top of the old city. The tour takes you through about 5 or 6 blocks underground while they tell you the colorful history of the city. The last time I took this tour it was $12 per person but that has been at least 3 years.
Mt. Rainier is 2 hours away.
The Space Needle provides great views. It cost about $15 per person to go to the top.
The Duck (amphibious boat) is a fun tour.
Walking the city streets is wonderful and lots of great neighborhoods.
The city buses are good in Seattle
Things to see in San Francisco
Top of the Mark hotel offers great views
The Trolley Cars are worth the wait in the line to ride.
Lombard street zig zags its way in town. A fun street to drive down.
Chinatown is great.
Fisherman's Wharf is not to be missed.
The tour to Alcatraz is very good
Things to see in LA:
Not sure where to start. Such a large city.
The drive from LA to San Francisco is not to be missed. Stop for lunch in Santa Barbara, tour the Heart Castle in San Simeon-- you will learn a great deal about America, stop in Carmel and Monteray--- actually you should spend at least one night if not two. 17 mile drive is the best! Napa Valley and Sonoma Valley's are close to San Francisco if you want to go taste some wines.
There is a trolly that drives up and down the strip all day long. You can hop on and hop off. One day our goal was to go inside all the major hotels on the strip and check out the lobbies. It took all day because we would stop for drinks or whatever.
Lots of shopping, swimming pool and shows. Amazing shows.
At the Grand Canyon you can make plans in advance and hike down, take a burro down or fly over in a helicopter. Sitting on the south rim and doing nothing is another great option.
Denver is a fantastic city located in the foothills of the Rocky Mountains. It is a fantastic city. Two hours in any direction provides you with options for hiking, biking, canoeing, skiing.
The Canyons of Utah are well worth a visit if you have the time.
The United States is a very large country. Your plans cover hundreds of miles.
Indianapolis is a fantastic city. I'm glad you are going to Peoria. Too many people come to America and not see any small towns. America is all about small town America.
Memphis and New Orleans are music cities. You will have a fantastic time.
If you drive you can add cities like Jacksonville and Savannah.
You will be here during football season so if going to an American football game interest you.
Ask some specific questions and I can answer them.