There are three Expanded Universe series that function very well as sequels to the original Star Wars trilogy and are valid alternatives to the Disney films.
The Thrawn Trilogy, starting with Heir to the Empire, was the first “big event” set after Return of the Jedi. It feels like a logical continuation of the story, progressing the personal lives of the main characters, adding to the secondary cast, and depicting the next stage of the war after the Empire’s defeat at Endor. However, it reads primarily as military science fiction and lacks the underpinning mysticism and philosophy of the Original Trilogy, and the movie characters, while well written, don’t go through much of a developmental arc. Consider this more of a “what happened next?” plot-centric sequel.
The Dark Empire trilogy, consisting of the comic series Dark Empire, Dark Empire II, and Empire’s End, feels in some ways like a counterpart to the Thrawn books. The plot is large, bombastic, and frequently silly, but it takes a back seat to the themes, philosophy, and character growth. Luke finally faces the temptations that ensnared his father and confronts the darkness within himself, while Leia embraces her Jedi heritage and takes up a lightsaber against evil when Luke is unable to. Consider this more of a sequel in terms of continuing the themes of Force mysticism and confronting the Jungian shadow established in The Empire Strikes Back.
Lastly is The New Jedi Order, a 19-book series beginning 21 years after Return of the Jedi. With the Empire defeated, the New Republic in power, and Luke’s reformed Jedi Order 100 Knights strong, the galaxy faces an existential threat in the form of alien invaders from another galaxy. The children of the legacy characters come of age in a war against an enemy who challenges their preconceived notions about the Force and the limits of Jedi philosophy, while the disparate power factions of the galaxy must unite or face extinction. Consider this a generational sequel, where the Original Trilogy characters still play major roles but the focus is equally on their children, and the mantle of galactic heroism passes from one generation to the next.
So these three series can adequately replace the Sequel Trilogy in terms of offering what good Star Wars sequels should have: continuation of the story, further character growth, expanded exploration of established themes and philosophies, and the coming of age of the next generation. Not that there aren’t other good and important post-Return of the Jedi EU stories that take place before and between these ones (Shadows of Mindor, the X-Wing series, the Jedi Academy Trilogy, and the Hand of Thrawn Duology, just to name a few), but in terms of being good sequels, these are the big ones to check out.