The best adventure games like Banjo-Kazooie are Yooka-Laylee, Donkey Kong 64 and Super Mario 64. Below are 5, each with the reason it is here — and, at the end, what filtering to adventure costs you.
Filtering to adventure means the place and the story are what you want back, not the challenge. It is the right filter when the thing you remember is where you were rather than what you did.
What you get: A world with a reason to wander it, and writing that survives being read rather than skipped.
What made Banjo-Kazooie worth playing in the first place is covered on the full list. This page is the adventure part of that answer, and only the adventure part.
By much of the same team — the direct attempt at a successor.
Rare's own follow-on, bigger and far more indulgent about collectibles.
The template Banjo refined, and still the tightest movement of the era.
Same engine and team, aimed at a completely different audience.
The collectathon with genuinely great writing and level concepts.
Mechanical depth. Several of the best adventure games have combat that is deliberately unsatisfying, because they want your attention somewhere else.
Specifically, these are strong answers for Banjo-Kazooie that are not adventure games, so they are not on this page:
The full list is on games like Banjo-Kazooie — 9 picks, no genre filter.
Yooka-Laylee. By much of the same team — the direct attempt at a successor.
No. Banjo-Kazooie released on the Nintendo 64, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Anywhere the story and the place matter more than the skill ceiling — point-and-click, walking sims, narrative thrillers and most open worlds. The label alone tells you very little, which is why each pick here says what it actually is.
They split hard. Open-world adventures run to a hundred hours; the narrative ones are often finishable in an evening, and the short ones are usually the better written.
By hand. Each pick was written for the full Banjo-Kazooie list first, on what the game actually does, and this page is the part of that list that is adventure — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the adventure guide for where to start in the genre generally.