Unsure about quaint but Discworld is absolutely pleasant and grows a delightful lore around itself. General advice is skip the first two (Pratchett was just figuring it out) and come back to them when you already love Rincewind.

For pleasantness and YA high fantasy vibe Le Guin's Earthsea Cycle is great.

For wizard school with a much more mature tone R.F. Kuang's Babel is a great read. Warning though it is much darker and heavier, so prepare yourself emotionally haha.

EDIT: was recommended that I give a heavier content warning to Babel which is fair. While it is thrown around as an HP alternative it is emotionally harrowing, has some extremely violent and disturbing sections, and is generally focused on depicting the horrors of colonialism. A good read, but prepare yourself going in and don’t expect it to be quaint or pleasant.

Less ... bigoted? Were there themes of bigotry in Harry Potter that I missed? Or are you simply looking for a better-regarded author?

Brandon Sanderson Cosmere fits the bill and is super easy to get into.

The Mistborn series might fit your description the most. But my personal favorite is The Stormlight Archive. The Stormlight Archive is what got me back into reading.

What makes the Cosmere so easy and enjoyable to get into is that different series are only vaguely connected. They take place in the same universe but on different worlds or realms. But since they share the same creation "myth" there are similarities between these worlds. When getting started a lot of the connections feel more like an easter egg. An easter egg that teaches you about the history of the universe.

But each series is basically self contained. Most characters and people aren't even aware of the existance of these different worlds. The focus is mostly on the specific world. Meaning you don't have to worry about reading order or missing out. Heck, if you don't enjoy a specific series you can even skip it without losing too much.

There are a few unpublished or planned books that will focus on the connection of these worlds, on characters that travel between them. They will probably be the most enjoyable if you read everything in the Cosmere.

His Dark Materials

An obvious choice for me is The Hobbit. It hits a completely different and more adventurous feeling to LoTR, while still hinting at the lore that would follow. Sometimes I think I might prefer to LoTR in general tbh.

The Discworld series might be what you're looking for.

The Amber Chronicles by Zelazny

Branden Sanderson has a bunch of good series that fit the description.

His Dark Materials aka the Golden Compass books

Raymond E. Feist's Magician series was quite engaging, I thought... though I read it many many years ago.

The Bartimeaus trilogy was really good

The David Eddings books are excellent.

The Daevabad Trilogy by S.A. Chakraborty was very enjoyable. Still YA, but engaging throughout.

Percy Jackson... kind of? Still a tad childish.

I was quite a fan of the Keys to the Kingdom series by Garth Nix when I was younger. The imagery is vivid, the characters are complex/capable, and the setting is an acid trip of wide-ranging allegory and symbolism.

If you’re looking for something less childish (or not YA) and less bigoted, I would suggest not thinking just in terms of series, but in terms of prolific authors.

People have mentioned the Discworld series, which is a series in the loosest sense of the word. They occur in the same universe and the books share characters. There’s individual storylines with min the series as well (eg the Witches books). You can start pretty much anywhere because each of the books is self-contained, and when you do stumble across, for example, the origin story of a character you liked from a novel where they were appearing as a costar, it’s always a bit more fun than if you had worried about getting all the backstories down in the first place.

I’d also recommend Neil Gaiman. His works are even less collected than Discworld, but there are commonalities and shared mythologies that make them feel coherent. Good Omens is where I’d start - it’s a feel good rom com about the antichrist and the end of the world. American Gods. Graveyard Book. The Sandman series is pretty brilliant both as a graphic novel and as a full-production audiobook. He has a ton of other work, too.

Neal Stephenson’s Baroque Trilogy is a compelling piece of pretty accurate historical fiction incorporating the great figures and events in science and politics of the 18th century (Newton, Leibniz, Hanover, the English civil war, Hooke, cryptography, natural philosophy, puritanism, capitalism, and so on). In total it runs a bit over 2000 pages. It’s not high fantasy though. It’s more like historical (science?) fiction.