Traveling Around in the US
Hitchhiking is quite frequent in Europe, especially students hitchhike a lot. I recall my student years, with a friend of mine travelled all over Europe, hitchhiking through Hungary, Austria, Germany and Denmark and back, well over 4000 km within a week. I'm not saying this is not possible in the US, but it's not usual. There are far less hitchhikers in the US than in Europe.
I think the reason for this is twofold. First of all cars in the US are far more cheaper than anywhere in the world. Gas prices in the US, even with the current rising prices are only half of most of the European countries. The income level is higher than in most of the countries, so anyone can afford a car. For a few hundred dollars you can buy a workable car which will take you from one coast to another. Why hitchhiking, then?
The other reason is the public safety. America is a quite agressive country. It looks nice and well regulated from the surface, but it can be very brutal. There is a lot of agreessivity in the TV and in the news. Because of the high level of crime in some regions police is trained well, and if someone does not obey them situations go very easily out of control into the extreme. Because of the agressivity in the media (and I guess in real life too, sometimes) pople in America are reluctant to stop and take strangers from the road. I wouldn't stop myself in most cases. I reall one single case in the last 2 years when someone tried to stop me to pick him up from the entrance of the freeway.
So my advice to you if you are coming to visit America is this: don't plan to hitchhike. People don't use to do this here, plus it's about your personal safety as well. You don't know who is the person who picks you up.
Instead of hitchhiking rent a car. For about $50 a day with insurance and tax included you can go whereever you want to go. If 4-5 people share a rental car, it will be really cheap and you can see America in a more civilized manner.
Greyhound Bus Lines
Greyhound is the name of the long-range bus service in the US. It is the cheapest transportation service in the US. And according to the price level the quality of people who ride the Greyhound is usually low. Or better said there is always a low class on the Greyhound buses, and in many cases vicinity of the Greyhound bus stations is are very unsafe from public safety viewpoint. Check for e.g. downtown Atlanta and you will see what I am talking about.
Shortly said: if there is not absolutely necessary, if you can find other ways to travel, don't ride the Greyhound. I have first hand experience riding it, and if possible I am avoiding it. Based on my experience the bus drivers are in most cases unfriendly, the public safety on the bus is questionable, and the long ride si exhausting. Imagine riding the bus for 3-4 days and night going from one coast to another, with 1-2 hrs stops a few times a day. It's not fun. Try instead the train, Amtrak, it's much refreshing.
But if you don't have other choices, then use Greyhound as a last resort. The only good thing about it is that it is cheap.
Amtrak Train Service
The Amtrak Rail Service offers a higher quality service then Greyhound. Thus it will cost you more. You might consider the airplane as an alternative. Sometimes you can get really good deals on flights (e.g. coast to coast flights, roundtrip Los Angeles - Florida $150-200 or lower with last minute trips, which is cheaper than Amtrak). But riding the train is fun. You can see lot more than from the plane. So if you have the time and want to see America then Amtrak can be an option.
A short time ago was Amtrak on the news headlines again. The company is deficitary and needed a $200 million funding from the government to stop working. Yes, Amtrak was at a step from bankrupcy and from final stop. But thanks to the government Amtrak is still running.
Renting a Car
If you really want to see America this is the best option. You can go whereever you want, you can stop whenever you want. It is a relly cheap alternative if more people share a car or a van. Please go to the rent-a-car page for more info on renting a car.
This is really popular in the US. There are tens or hundreds of thousands of people who are flying daily. It is the fastest way to travel and sometimes it might be the most economical one, especially on longer distances. Thus is not uncommon that with less than $200 you can fly roundtrip coast to coast.
Another very good option to fly are the last minute deals. When airplanes can't sell all the tickets for a flight, instead of flying half emplty, they offer last-minute-trips right before the flight. This means for about $50 you can fly with the flight to the destination. If you have to be somewhere in time than don't count on the last minute deals. Yuo never know when you find last minute deals. You can try your luck, but don't count on this.
Recently some internet companies started to advertise last-minute deals. Not only flights, but complete last minute packages, flight with lodging. You can get incredible deals on the internet. Just to give you an example with my wife we got an e-mail one afternoon about a few destinations for the upcoming weekend. We picked up a San Francisco weekend trip, Los Angeles - San Francisco roundtrip flight, including 3 nights in Crown Plaza, a very nice hotel, all for about $170 per person. We decided from a day to another that we want to go and we spent 3 beautiful days in the scenic San Francisco and Napa Valley. The best places to look for such last-minute deals are Orbitz, Expedia and Priceline. You can subscribe to their mailing lists and they send you weekly the last-minute deals right into your mailbox.
A few words about airport safety and check-in. Since the 2001 September 11 terrorist actions the airport safety became tighter and the checkin process longer and more painful. Even for domestic flights. I recommend you to be at the airport at least two hours before the departure. Sometimes are very long lines at the security check-in point, sometimes are not, you never know. If you take personal luggage onboard be prepared to get through a second safety check before boarding. Most cases you have to take off your shoes, the security checks your shoes as well. If you have a laptop you will have to take it out from the bag. All the bags are checked thoroughly, and this slows down the boarding process.
If you are driving your car to the airport and plan to leave it parked at the airport be aware that parking fees around the airport are very expensive. You can easily count $30 per day. So you might consider as an alternative to leave earlier from home, park somewhere not very close to the airport in a cheap parking lot and take a cab or bus to the terminal. It might be cheaper than parking you car for days right at the airport terminal.