Mrs. Piggle-Wiggle?
And if that’s not the answer, it’s still a fun series of books that answer the OP question!
Certainly The Hobbit now, as a way into LOTR in another couple of years, should work.
How about the Lemony Snicket books? I’m not sure what age level they are intended for, but I think they’re probably advanced enough to keep him interested. Also they’re kind of subversive compared to other kids’ books, which I think is a good thing.
Since he’s read Harry Potter, Tamora Pierce’s Circle of Magicbooks might be an option- those first four are fine, no sexual content at all. There are \minor hints in the second set of four books, the Circle Opens books (and significantly more in the Will of the Empress and Battle Magic books - those are single books each, though connected).
Because sexual content is an issue, stay away, for now, from her Tortallbooks. Those do have sexual content, whether or not the characters actually have sex.
The only sexual content in Pratchett, especially the earlier ones, are sideways references to the Guild of Seamstresses. Nanny Ogg is a bawd, but unfortunately for her there is never a man under her bed, no matter how hard she looks. 
Seconding the Prydain books. One of the best fantasy series ever.
Angie Sage’s Septimus Heap books are really fun even for an adult. They are consistently a little younger than the later HP books, so they are easier, but I think they are still engrossing.
The Chrestomanci books by Diana Wynne Jones, starting with Charmed Life might be perfect.
The Sammy Keyes books by Wendelin van Draanen, starting with Sammy Keyes and the Hotel Thief. It’s not fantasy, but it’s fun and brisk mystery.
Or the Alcatraz books by Brandon Sanderson, starting with Alcatraz Versus the Evil Librarians. More of an urban-ish fantasy.
Oh, nearly forgot the Skulduggery Pleasant books by Derek Landry. Although this would depend on whether he was sensitive. If he’s sensitive, not the best choice. There are definitely very scary things in this one, and death. I don’t think it’s too much for a kid who handled all of Harry Potter, though.
And the Theodosia books by RL LaFevers, starting with Theodosia and the Serpents of Chaos. Fantasy mystery.
As a kid, I read the entire Wizard of Oz series, and really loved it.
Most people don’t know that there were fourteen books!
Maybe Scott Corbett’s series of books with titles in the format The ______ Trick ?
So did I. (There were more written by other authors who continued the series after Baum’s death, but I only ever read the Baum books.) They’re now in the public domain, so you can find free or cheap electronic versions (some of which do and some of which do not include the original illustrations).
Former elementary school library volunteer here…
The Percy Jackson books are much much better than and substantially different from the movies. The horny satyr and Persephone were strictly for the movies - the movies aged up all the characters to their late teens, presumably to make casting easier. In the books Percy ages from 12-16, so there’s nothing more than kissing. (Well, that and the backstory of gods coupling with mortals). The books were very popular with the 3rd and 4th graders. If he could manage Harry Potter he should have no problem. I’m an adult and I enjoyed them once I made it through the massive exposition dump in the early part of the first book, which is where most of the Harry Potter parallels crop up. Once that’s out of the way, the series becomes its own thing.
Another recommendation for the Chronicles of Prydain.
At 10, I really enjoyed John Christopher’s White Mountains trilogy. Fun post-alien conquest of Earth science fiction series.
I haven’t read them, but the 5th grade classes were nuts about the The Seekers books. I was constantly getting requests for those, only to have to say “Sorry, all copies are already checked out”.
For some reason, the third graders were obsessed with the Geronimo Stilton books. I found them kind of dull, and they might be too simple for some one at your nephew’s reading level. But there are over 30 in the series, and that shelf usually was cleaned out after every 3rd grade class.
On my 11-year-old’s recommendation I’m about to start Susan Cooper’s The Dark is Rising sequence. The 4th one won the Newbery Award
For a 7 year old, I’d recommend Sun Tzu’s “The Art of War” and Machiavelli’s "The Prince.
Is the Dr. Dolittle series still available? I read those books as a child and loved them.
My kids loved the Eragon books by Christopher Paolini and Philip Pullman’s His Dark Materials trilogy.
My now-college-aged daughter, who loves the Percy Jackson books, says to tell you that she hated the movies and not to judge the books by them. She also says she read The Giver when she was seven (and again in middle school) and recommends it.
Oh, and for some more oldies-but-goodies (as well as the Oz books and Dr. Doolittle), we both recommend The Borrowers by Mary Norton and My Side of the Mountain by Jean Craighead George (both of these also have sequels).
Neither of us is very sure what age range any of these books is specifically written for, but if your nephew has read and enjoyed Harry Potter, these all should be somewhere around the same reading level.
That is indeed it. I was thinking of “The Lemonade Trick” and “The Limerick Trick.”
Thanks for all the suggestions. I’ll be in the bookstore tomorrow and I’ll look around for them.
I admit, as a kid, I never read much fantasy, so I’m a bit short on that front—but I can second that The White Mountains recommendation.
I really like “A Wrinkle in Time,” but I don’t like the rest of the books at all (and I gave up on the series after the third one). I do remember being very fond of “The White Mountains” when I was a kid.
I’ll probably get him the Percy Jackson series, since that’s current, and get him “The White Mountains” series so that we have something to talk about if he has questions about it. But I will check all the suggestions out while I’m in the bookstore tomorrow.
I wonder if a kid nowadays would like “The Great Brain” series, which I enjoyed as a kid? But it may not have enough fantasy or adventure for kids today.
Have a look at the Leviathan series. Steampunkish adventure set around an alt. history WW1
I would hesitate to railroad him into the fantasy genre already. Maybe you could get him a collection of standby childhood classics like Johnny Tremaine, Charlotte’s Web, Old Yeller, Where the Red Fern Grows, Cricket in Time Square, Call of the Wild, Hatchet, Wind in the Willows, etc.
Or a Roald Dahl collection.
Golly, no love for Encyclopedia Brown?
Ha! I like Encyclopedia Brown. Me and my friends used to make fun of it, though, because most of his plots revolved around catching someone in a fib, which of course meant they were guilty of whatever crime had happened – because nobody would ever fib about anything for any reason, unless they were guilty!
Of course, that’s pretty much the plot of every “Murder She Wrote” episode, so perhaps we judged Mr. Brown too harshly.
Heck, if we’re including mystery series’, I could be here all day. But Bellairs’ Johnny Dixon series actually includes the supernatural to some extent.
'Might be a bit too much gothic horror, though, depending on the 7 year old in question. I mean, I loved 'em, but…
With illustrations by Edward Gorey! Joy! 