The Once and Future King (White). The first book is, rather like the Hobbit, an introductiory book written for (but not purely for) children.

The rest of the series is more for adults. They have a good mix of action (battles, quests etc.) and political intrigue and background.

The final volume adds aclever and interesting twist.

And then of course I recommend the Narnia books by C.S.Lewis. I know Tolkien wasn't really happy about some aspects of these, but I think he wouldn't have been happy about a lot of modern fantasy.
These books contain certain parallels to Tolkien's sub-creation, which isn't surprising seeing both men were Inklings. Tolkien also scorned Lewis for his religios views, and this may have led him to judge his works rather too critically. I think they make good reading for both adults and children.