Public transportation

We will be spending 2 weeks during August in Japan using JR pass. My wife and I will be visiting Tokyo, Takayama, Kiyoto, Hiroshima, Fuji and more. How easy is the use of public transportation when you get to cities? What trasportation to use in Takayama when you get there with the train? What about Kyoto? What are the prices of taxis in those locations? Isn't it too expensive to use taxis to go from attraction to attraction? What about renting a car when you get to those places? Thank you, Motty

How easy is the use of public transportation when you get to cities?

It is quite easy, especially if you prepare in advance.

What trasportation to use in Takayama when you get there with the train?

Most of Takayama can be navigated on foot:
http://www.japan-guide.com/e/e5908.html

What about Kyoto?

Buses and subways are the easiest way to get around:
http://www.japan-guide.com/e/e2363.html

What are the prices of taxis in those locations?

Generally speaking, the base fare (for the first two kilometers) is around 500 to 700 yen. Afterwards, the fare increased roughly 100 yen per 500 meters, but the details depend on the city and taxi company.

Isn't it too expensive to use taxis to go from attraction to attraction?

Depends on your budget. If you travel in groups of three or more, taxis can be very economical over small distances. They tend to be considerably more expensive on longer distances, though.

What about renting a car when you get to those places?

It is not recommended in the cities. Only in the countryside.