Travel to the United States and Away
Unless arriving from Canada or Mexico it is best to fly to the United States. The largest major international air hubs are in New York, Miami, Houston, Los Angeles, Washington DC, and San Francisco. Flights to and from the East Coast to Western Europe are priced seasonally and usually range $500 to $1000 (purchased from the major online ticket agents.) Flights between Asia and Los Angeles or San Francisco are a few hundred dollars more and less dependent on time of year.
The border with Canada is porous and easy to cross although this has changed some post 9/11. There are border stations with passport requirements but wait times are usually minimal.
The Mexican border is much more interesting. Anyone is allowed out, but huge waits can be found on the Mexico entering into the US in cities like Juarez and Tijuana. Imagine what borders in Europe would be like if there were no Mediterranean isolating Northern Africa.
Travel around the US
This is where the difficulties arise. The highway system is excellent, but heading out west the destinations are significantly spaced out. Increasing gas prices can make this option costly. Flights are timely and easy but relatively expensive. The bus and train system works for the most part, but service can seem limited, and costs more than it should.
Buses do run just about everywhere. Greyhound offers fares as low as $30 for trips planned in advance. Trips can be booked via the web as well.
You can travel on any day between any major city, just don’t expect the phenomenal deals found for commuter flights in Europe. Stand-by flying, or just showing up at the airport, the day you want to fly in general does not work. There are some rumors that one can try and fly as a courier cheaply, hand-delivering packages, but this option is probably limited to US citizens.
Probably the best option, you see the countryside and have more input on where to steer the vehicle. The roads are in good condition, well marked, and for the most part it is easy to get gasoline and food just about anywhere. Roadside hotels run about $50 a night with tax. One can purchase a used car pretty cheaply ($1000-$2000) but be sure the paperwork is in order. Police go by the book and routine traffic stops are part of money-making schemes on the county level. Rental cars can be as cheap as $30 a day with no additional cost for miles driven (Enterprise, Hertz.)
Sadly, the country that produced On the Road is terrible now for hitchhiking. There are many laws against it, few places to stop along the multilaned interstates, and worst of all a general fear in the population about picking up hitchhikers (they must be murderers or at the least lazy non-working bums.)
A replacement to hitchhiking, one can arrange rides city-to-city on internet bulletin boards. Erideshare.com is a popular venue for this.
In the suburbs and smaller cities you are screwed without a car. Americans drive all the time for everything, even to go and buy a pack of cigarettes at the corner store. Newly developed areas and western cities have many areas that don’t even have sidewalks. Walking or riding a bicycle can be inconvenient in many places or downright dangerous as drivers are not used to seeing pedestrians on the larger roads.
The better cities have well developed bus systems that usually bring you anywhere along the line for a dollar or two. Riding the bus, in a city like Los Angeles, connotes a low social standing.
Safe but on the expensive side.