I remember thinking through the potential evolution of autonomous transportation* some 10 years ago, and, barring the protectionist forces winning out and enshrining the "right to drive" in law, like the "right to bear arms", it's pretty clear where the transportation is going.

1. One- or two-person electric commute vehicles dominating city traffic, eventually leading to the whole swaths of urban areas being closed to human drivers, which would be deemed unsafe. Those areas will then expand outwards and merge, eventually spreading into the suburbs, and at some point major highways, first with HOV lanes, then taking over the rest lane-by-lane. Owning a car will become very expensive, and a human-driven car prohibitively so.

2. The huge parking lots will disappear, since uber-like electric commuters will be in use much more often and can be stored efficiently in much smaller spaces during off-peak times.

3. Everything will be routinely recorded, whether outside of the vehicle or inside it, limiting the type of activities one can indulge in while getting to the destination. Vandalism will virtually disappear, as well. Ride sharing will complete strangers will be as safe as walking along them on a busy street somewhere in central London.

4. Once there are no more human drivers, in the autonomous-only areas the vehicles themselves will be able to communicate and coordinate, and soon will be required to do so, forming a driving grid. Any vehicle not complying with the grid inclusion rules will not be allowed in, or forced to stop and get towed outside. Yes, the grid will eventually take control from the single vehicles.

5. Once that happens, the traffic lights will be largely obsolete. There will be pedestrian crossings, with the Walk/Stop signs, but no usual traffic lights, since there will be no human drivers to look at them.

6. The current alternating pattern of driving through the intersection will change: without pedestrian crossings cars will simply zoom in all directions, their movement perfectly choreographed by the grid. With pedestrian crossings there will be breaks for humans to cross on foot in all directions at once. Odds are, many crossings will be replaced with walkways above or below ground.

7. Congestion will be greatly reduced due to coordination. Worst case you'd have to wait to get your ride, as the grid will limit the number of vehicles to keep the system at peak efficiency. Traffic jams will be extremely rare, since most current causes of it will be eliminated, such as broken down cars, accidents, high volume traffic, power outages, road work (the grid will shape the traffic around any roadwork in progress).

8. The city architecture will change to accommodate the new transportation realities: there will be much less road space needed, so some of the wide busy streets will be repurposed for parks, living spaces, etc.

This is as much as I recall offhand, but there is definitely more.

Now, to answer your question, the costs will eventually go down orders of magnitude compared to the existing means of transportation. Which does not mean that price will go down nearly as much, as everything will be heavily taxed, like train and plane tickets now.

Edit: I expect this will happen first in places with high penetration of autonomous vehicles. Places like, say, Oslo. Also in the countries where the government can exert some pressure and ensure compliance and coordination, like, say, in China and maybe Japan. The US will be one of the last ones, and the most expensive ones, as is customary with most technological innovations lately.

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* The language will evolve accordingly:

"self-driving car" will be a name for DIY driving, the opposite of what it is now.
self-driving will be reserved for antique car enthusiasts, who would tow their cars to a "driving range" and show off their skills in this ancient activity, sort of like horseback riding is now.