getting around czech republic

https://jizdnirady.idnes.cz/vlakyautobusymhdvse/spojeni/
this is the website I use for transport within the CR. There is an English link about 1/3 down the page.
Covers local national trains buses and trams.
Prague to Plzen can be done by train or bus and 4 euros seems slightly cheap, though it has been over a year since I have done the trip and I did it by train on a day return. Plzen to Nuremberg buses would be run by the train companies and that price seems about right though I have not done that trip, there is a direct Prague to Nuremberg bus run by dBahn.
Also check the website of maninseat61 which is great for all info on trains in Europe.

Also check Student Agency for inter-city and inter-country routes. Sometimes nice to get the train one-way and the bus back if the price is better. https://www.studentagency.eu/en

You can get a summer ticket - Jízdenka na léto - with Czech Railways. These are special train tickets that allow for unlimited train travel within the Czech Republic for either 7 or 14 days (790czk and 1190czk).

Hi from Wisconsin,
You may have already traveled, but for trains in Czechia go to www.cd.cz Great prices, 50% or more off other websites.

wayne iNWI

I have done Prague to Pilzen and Nuremberg to Prague, both by train. Cost wasn't that much different than what you sited. Those are fairly short trips. I prefer the train as it's faster and less crowded than the bus.

Actually from Nuremberg to Prague bus is faster and it's run by Deutsche Bahn (German Railroad). It goes from the train station in Nuremberg to train station in Prague and it's nonstop.