Do you really want to visit only castles?
Peles is usually closed in November, unfortunately.
Public transport to/between the major sites mentioned above is good, no need to rent a car.Edited: 10 June 2018, 07:04
The absolute must see is Peleș, but it is indeed closed in November every year for maintenance. It's most likely going to be closed November 1-30, but check back a bit later when they officially announce it.
Next to that, a popular castle to visit is the Bran Castle, commonly known as Dracula's Castle. If you do visit Bran, be sure to also stop in Râșnov to visit the fortress there, it's also interesting and medieval. A bit further away from the main tourist areas, but still impressive is the Corvin Castle.
And the other must-sees are the main medieval cities of Transylvania - Brașov, Sibiu and Sighișoara. Try to also base yourself in these cities, especially if you use public transport as the first 2 ones are big transport hubs of the region.
Public transport in Transylvania is good compared to other parts of the country. You can rent a car for extra flexibility and more time to visit, but all the sites mentioned and many other interesting things to see can also be reached via public transport.
Thank you. We love medieval: castles, knights, etc. We could possibly extend our trip until December 2 nd if that guaranteed we could see Peles. Thank you again for all of the advice. We are open to seeing other things besides castles. I am happy to learn public transport is sufficient in Transylvania!
Peles reopens on November 30th or December 1st, so yes, you could see it if you extend your stay a bit.