"I was hoping to take the train from Bayreuth to Nuremberg, but when I searched there was none found?"
Search HERE:
https://int.bahn.de/en/
Enter date, time of departure, # of travelers, Bayreuth Hbf as your "from" station, Nuremberg as your "to" station.
You will find schedules as Sam described. It is a simple, direct train ride of roughly one hour on the Regional Express train. You might not find schedules if you are searching for a date in the very distant future.
DO NOT BUY TICKETS IN ADVANCE. Regional trains do not offer seat guarantees or reservations and you get no discount for pre-purchasing - only a ticket that is non-refundable. So just chill and buy your ticket when you get to the station that day. Traveling by regional train is super easy - just get your ticket from a ticket machine at the station (or using the DB app) - machines will have an English-language option - then get on and ride. Keep your ticket in case a ticket inspector requests to see it.
The Tagesticket Plus which Sam mentions is perfect for you. It's a day pass costing €26 (level 10 price) or so and good for any trips you want to make all day long on any trains withn the VGN travel zone (which your trip is within.)
https://www.vgn.de/en/tickets/all-day-ticket-plus/
Stations will have signage indicate train destinations, platform numbers, departure times, etc.
If I'm not mistaken, Rick Steves guides offer information on getting to the Documentation Center / Rally Grounds, the Nuremberg Trials courthouse, etc.
https://tourismus.nuernberg.de/en/discover/museums/location/documentation-centre-nazi-party-rally-grounds/
https://tourismus.nuernberg.de/en/discover/museums/location/memorium-nuremberg-trials/
I don't go in much for the WW II museums - Nuremberg has other fun museums that might be more entertaining:
https://tourismus.nuernberg.de/en/discover/museums/science-technology-museums/
https://tourismus.nuernberg.de/en/discover/museums/unusual-museums/
Main website:
https://tourismus.nuernberg.de/en/
You can visit the Imperial Castle too - right in the old town zone:
https://www.kaiserburg-nuernberg.de/englisch/tourist/index.htm
https://tourismus.nuernberg.de/en/discover/places-of-interest/location/imperial-castle/
The Tagesticket Plus you bought to reach Nuremberg will get you anywhere you want within the city on buses, trams, and subway as well.