The best adventure games like Batman Arkham Asylum are Batman: Arkham City, Marvel's Spider-Man and Middle-earth: Shadow of Mordor. Below are 9, 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 Batman Arkham Asylum 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.
The sequel, opened into a district, and the best of the four.
The same combat lineage with the best traversal ever put in a city.
Freeflow combat plus a nemesis system nothing else has matched.
If the one-building-that-opens-up structure was the real appeal.
Gadget-gated traversal with a combat system that asks more.
The best non-Batman freeflow combat, in Hong Kong.
For the predator rooms — patience, observation, and a plan.
A building that is a character, and powers to tear it apart with.
Stealth where being seen is a choice you made, not a failure.
Mechanical depth. Several of the best adventure games have combat that is deliberately unsatisfying, because they want your attention somewhere else.
The full list is on games like Batman Arkham Asylum — 9 picks, no genre filter.
Batman: Arkham City. The sequel, opened into a district, and the best of the four.
No. Batman Arkham Asylum released on the Xbox 360, 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 Batman Arkham Asylum 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.