Hi Mansun and Kitanna,
I think you're pretty much right on the hobbits. Most didn't learn to read and write (mentioned in LoTR), the Gaffer worries that Sam being taught by Bilbo might give him 'ideas above his station'. (Which luckily it does
).
I wonder if the wealthier hobbits (eg Merry and Pippin) were taught by personal tutors? But agree that learning could easily be passed down in the family. There are no mentions of schools in Middle Earth that I can think of, perhaps Gondor might be the likeliest place if any existed?
Certainly the Gondorians and Dwarves were quite well educated, I guess anyone involved in trade must have had some of the 3Rs, eg the Lakemen, Sandyman, Saruman's human servants etc. Rohan appears to have more of an oral tradition (also the Beornings?), not to say that this isn't learning of course, but just a different way. No doubt the nobility of Rohan were literate and Grima seems a classic 'scribe'.