You hit the nail on the head. I also remember McCaffrey's books with great fondness, but with the realization that I've outgrown them. At this point, I think the only one I'd recommend is the little-known "Restoree", and maybe "To Ride Pegasus".
Avoid the space unicorn at all costs (look up "Acorna" on Amazon - the cover illustration gets it about right)because the basic concept is just too pre-adolescent for an adult to enjoy.
If you can get through "Dragonflight", which is excellent considering when it was published, the next two books in that trilogy (Dragonquest, The White Dragon) are pretty decent for the political/societal world-building content. Just be aware that McCaffrey really liked pairing people off, and there's no homosexuality in her world (again, consider when the books were written). Other than that, you'll probably find the books not sophisticated enough to really enjoy.

I have to admit that the excellent quality of quite a lot of fanfiction has actually spoiled me for a lot of published authors.