Hi,
Sorry to dash your hopes of buying that dirt cheap car. But we do stand by what we say. The fact that you are both under 21 would contribute to making your insurance rate high. In the U.S. that is still considered young and high risk.
At today's rate you are looking at having about $27 USD per day per person for your 6 month trip. The most expensive part of traveling can be the lodging. So by camping you will greatly reduce your expenses. You can also stay in a youth hostel. Hostels aren't as common here as in Europe. But they can certainly be a great budget saver. For example, a private room in New York City will cost you under $50. That's super cheap for NYC, one of the most expensive cities in the US. You can look online for hostels around the country here. http://reservations.bookhostels.com/usatourist.com/ Rates (and amenities) will of course vary by location.
As far as transportation, your budget options are train or bus. Our national train line is run by Amtrak. And our bus is Greyhound. www.amtrak.com and www.greyhound.com. Unfortunately the train service in the US is not as handy as in the UK. We could stand to learn a bit from you all! You can search for routes and rates on both sites. You should look into getting a Pass. On the Amtrak site go to Hot Deals then Rail Passes and Programs. They offer passes for various lengths. Be sure to read all of the details (restrictions) before purchasing a pass.
Greyhound has Road Rewards. They'll give you various rewards depending upon the amount that you travel. A link to the program can be found on their home page.
The two downsides of traveling by bus/train are time and convenience. It can take a good bit longer to get from A to B than if you were to drive. But since you will be in the U.S. for such a long time, this should not be a big issue. The bigger inconvenience is that you will be limited to where you can go. For example if you want to visit the national parks, you will likely have to find the nearest station and then find local transportation from there.
For traveling greater distances, I recommend looking at Southwest Airlines. You can get cheap one way tickets to destinations across the U.S. If you book at least a couple of weeks in advance you'll get cheaper rates. Look at various dates. Having a flexible schedule can certainly help save money.
Be sure to spend the time to do price comparison shopping. I did a search for travel between LA and Las Vegas for later this month (10/20). By train it was $39 per person. But Southwest had a rate that was $48 (web only). The shortest time the bus would take between the two destinations was about 5 hours. The flight is 1 hour. Even with extra time at the airport for security screening it is a better deal. The train was about $50 and was about a 6 hour trip. Register for Southwest Rapid Rewards for the possiblity of more savings.
Since you are camping, going to the grocery store and cooking your own meals will also be a budget saver. If you need a break, the grocery stores will also have ready made foods (hot and cold) that you can choose from. Depending upon the store, you may even find sushi and pot roast dinners! Of course more expensive than cooking something yourself, but less expensive than a restaurant!
Have a great trip!
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