Many Americans travel by air in their own country. Almost every medium-sized city has its own airport and there is intense air traffic. Prices are often lower than we are used to in Europe, but can quickly change as the flight date approaches. Therefore as a tourist any domestic flight(s) can best be planned and booked before you departure to the U.S.
For inland transportation the train was always in the shadow of the plane and car. But impressvie improvements have been made on the railway network. Nowadays it has a total lenght over over 40,000 km, with 500 destinations. The prices of tickets are slightly below the air fares and for tourists there are special rail passes, valid for a certain period of time. Trains are comfortable, spacious, not crowded and are operated by Amtrak, founded in 1970 and managed by the federal government. There are Long Distance Routes (over 380 miles) with sturdy names like “Silver Meteor” and “Texas Eagle”. The shorter Regional Routes have more stops.
There is also a category of commuter trains in the urban areas but this is less important for cycling tourists.
Within the U.S. bus travel is cheap but it takes longer. Buses are safe and they have become more luxurious in recent years. There is a dense network of bus lines. Greyhound Lines is the largest bus operator in the U.S. There is also a smaller company called Trailways. Greyhound tickets can be ordered online, but a seat on the bus is not guaranteed - it is therefore recommended to be present at a bus- stop well before departure. Trailway tickets can be bought at the bus-stop or from the driver.
Driving a motorhome or a car in the U.S. is no problem as a tourist. Rental cars are of good quality, there is a wide choice of models and rental depots. Road signage in the U.S. is excellent (routes are often indicated north-east-south-west) and roads are wide, well maintained and generally not very crowded.