First, the trip. That's much too long a list of destinations. You'd have at most 1 day in each place if you wanted to see all those places in 12 days since you lose almost a full day in travel going to each place. My advice: Pick your favorite three places and schedule 4 days in each; just realize that one of those 4 days in each place will be eaten up in transit.

Second, luggage. Simply don't bring much excess luggage. Pack as light as you can and buy all your toiletries here. Bring one bag no bigger than 24 inches (better 22 inches since that can be carried on most domestic flights) and clothes for 8 or 9 cays and plan on doing laundry; you can easily send your laundry out here in NYC or go to a self-service place. If you need some very summery clothes for hot weather, assuming you are in NYC for August and September, bring a few extra changes that are just for summer and expect to re-use some of your other lighter clothing by layering for the cooler periods. It may still be quite warm in LA, Las Vegas, and San Francisco and could be warm in Texas. It's so hard to predict this far ahead, but it should not be very cold. I only started wearing my cold-weather jacket today. Before the days have been in the 50s and 60s and have been much much warmer in some places further west.

You should probably ship the most summery clothes back to your conference hotel in Los Angeles (assuming they will hold it for you) since you'll spend a fortune checking extra bag throughout your US travels. Or send it back to Singapore, though it will take longer. Most conference hotels will charge you to hold a package, so do price everything out to see what your options are before making a final decision.

This is how I would do your trip by train and flying. Flyiong to New York - conference- take the train from Penn Station to Washington Union Station. If you want to spend a night in DC find lodging close to the station. The station is within walking distance of the Capitol Building. Leaving Washington take the Capitol limited overnight to Chicago. The HI Hostel in Chicago is great for cheap lodging. Take to overnight "City of New Orleans" to New Orleans arriving mid afternoon. From New Orleans, take the Sunset Limited as far as Houston Texas. If you go farther, you would arrive too late in San Antonio. From wherever you stay in Texas fly to Las Vegas since LV is not served by Amtrak. Rent a vehicle in LV to go see the Grand Canyon. Return the car to Las Vegas and take the short flight to LAX. If you have the time after your LA conference, you can take the Surfliner north to Santa Barbara or the Coast Starlight all the way to Emeryville with a bus connection to San Francisco.
If you can sleep in coach on Amtrak, you can save a lot of money compared with sleeping in a hotel room and not getting closer to your destination.
As long as your bag weighs less than 50 lb. and you can put it overhead it is OK on Amtrak.
Price 15 day USA Rail Passes and compare the standard fares for the trips you take on Amtrak. You may save money with the USA Pail Pass depending on the distance traveled by rail.

>>Texas (quoting my friend: great sights, explosions in the sky, BBQ ribs, explosions in the sky) <<

Explosions in the sky? Wouldn't that normally be a reason to avoid visiting?

There is no way you can see all of those places in the ery limited time that you have. It's a really big country. (2 hours from NYC is still the suburbs.)

I would pick 3 or at most 4 places and fly to them. (Train is NOT an option - it doesn't go many places is very slow and is often many hours late.) You could drive - but then you would be spending all of your time on the road. There will also be a big charge for dropping off on the other coast - as well as a cost for each additional driver. Finally - by October you can easily have snow in the mountains out west (and some roads/passes closed) - and if you have never driven in snow this is NOT something you want to do. Also - it's often very difficult to get a car rental if you are under 25.

Have no clue what explosions in the sky is about - but certainly hope you don;t encounter any - unless you mean fireworks.

We don't have any fall fireworks, you must be thinking of England and Guy Fawkes Day.

My suggestion: Start with New York. It's an amazing place and so much to do there. Then, 1-2 of you who are 25 or older rent a car and drive between New York and DC, and spend a full day at Hershey Amusement Park in Hershey PA. I have teenagers and we did a long New York/DC trip this summer. Their main regret is that we didn't get there earlier in the day. They thought it was a really great park and we've done a lot of California. Turn in the car upon arriving in DC (or perhaps a day after if there's a side trip you want to take). Fly from DC to Los Angeles for the the rest of your trip.

Plan B: Add Las Vegas/Grand Canyon but shorten your time back East.

I love Chicago but given the length of your trip, the cities are all going to blur together similar to when Americans do a six-countries in 12-day tour in Europe. I can't speak to Texas as I haven't been, but again, I think it's too many stops to really enjoy anything.

Regarding Lugggage: the OP is a fashion photographer and may also have the issue of camera equipment to transport. For your flight from Washington DC to LAX or Los Angeles, I would recommend you price the carrier Southwest Airlines. Currently they still allow you to check two bags free. (Doublecheck that the baggage policy hasn't changed when you book.) I'm sure you know to put any camera equipment in your carry-on.

Umm...meant to say LAX or Las Vegas...

but since I have to correct my post anyway, I will also mention that you can get some really good Southern Comfort food at Roscoe's Chicken and Waffles in Hollywood. Not the same as Texas BBQ but just mentioning it.

Actually, the OP can get a Texas-style bbq fix right here in NYC at Hill Country, which is pretty good and saves a trip to that state. Problem solved!!!

You can drive the 3,000 plus miles from NYC to LA in 2 days if driving non-stop, 24/7. Taking the newer (sort of) interstate 40 will get you for the most part, everywhere you want to go.

The fastest we've driven coast to coast, with overnight stops at cheap motels was a week. And even in a week, it's kind of exhausting and going through some states (not mentioning any names), kind of dull, boring, and GRAY!!

The train. Well, I love the train, and you can go from NY to Chicago; spend time there (great blues bars, fabulous city!); then take what used to be called the Super Chief from Chicago directly into L.A. It's called "super" something now.

I like Southwest Airlines. It goes to a lot of places and is reasonably priced.

If it were me and I wanted to go somewhere between NYC and LA, my preference would be Chicago. Big city. Plenty to do and see especially for people of your age group.

I have a personal hatred of Las Vegas -- I guess it's okay if you like to drink (I do!) and gamble (nah) or see an expensive show (some really good ones, and lots of cool bands play there these days, and that is the one big draw for me). But if that's your bag, fly NYC to Las Vegas. Then fly to L.A.

The train from Chicago to Los Angeles is the Southwest Chief.
These guys wanted to see Texas. The only way they will see explosions in the sky in Texas in October is if one of the baseball teams wins the World Series (not likely).It would be somewhat faster to fly from Chicago to a Texas destination and then from Texas to Las Vegas for the Grand Canyon and possibly using the LV rental car for the trip to Los Angeles and up the coast. East of Chicago the train is OK even if it is a couple hours late provided you don't have to make a connection going somewhere else. Spend at least 18 hours in Chicago.

"Explosions in the Sky" is a post-rock band from Texas, hence OP's linking them. I can't find any online info as to a 2013 tour.

Some of their music isn't so bad. A friend played some. I liked at least the one song.

Ahh, so glad you let us know, Propita.

Are you you guys going to the Hillsong conference?!

These are the conference dates:
NYC: October 4th & 5th 2013 // Radio City Music Hall
LA: October 18th & 19th 2013 // Nokia Theatre

--are you serious?!
Are you some entertainment mogul, or wanna be? Is Oprah the headliner?

12 days is a really short time period for travelling cross country

--no, just take the plane from LA to NYC, 5hrs non-stop.

New York
Washington
Chicago

--ok, besides D.C. which is a no-brainer, others you need a plan and maps.

Texas (quoting my friend: great sights, explosions in the sky, BBQ ribs, explosions in the sky)

--skip it on such short trip

Las Vegas (for the Grand Canyon, not gambling haha)
LA
San Francisco (maybe after the conference...)

--ye, the neon aint too impressive. In fact nature site seeing is better than the casinos.
LA+San Fran... well, too far from each other. See Hearst Castle. + San Diego.

Also, I wanna eat In N' Out Burger!

--I am a big fan of Five Guys. In fact, their fries are to die for.

Uh. What should I do with the excess luggage? Should I mail them back to Singapore first?

--whom, your friends? ye, ship 'em back to the mother country. who needs them bums?!

When you are done with the things you only need in New York ship them back to Singapore by DHL. http://www.dhl.com.sg/en.html
There is a lot in this country to see between Washington DC and Las Vegas. You can easily get from DC to Texas by train in 5 days. Fly from Texas to Las Vegas to go see the Grand Canyon.

Sure, you could do that, but then over half your trip is transit time (5 days train plus a day between NY and DC). I just don't think that is the best use of her time. If she were staying a month, it would be 1/6 of her trip and might be a nice break from sightseeing. Just