I'm not sure if you include SNES games in your search as well, from your post I would guess no, but in case that you do: you might want to check out
Lufia 2, a typical manga SNES adventure RPG, comparable to games like Chrono Trigger and Terranigma (especially Chrono Trigger). The main character is Maxim, a bounty hunter who fights monsters for a living. When more and more, and stronger monsters keep showing up, he starts to travel through the land to find out if anything is wrong, and what could be the source. Along the way, he meets a bunch of different NPC's who join his group, all with different personalities, and characteristically spells or fighting abilities. There is quite some fighting in the game, but it's turn-based with a different menu for the fighting, so that you maintain quite a clear view over the dungeons; it's not just a fighting fest of hack 'n slashing everything that comes your way. Also, many fights are avoidable (though you basicly do need the experience for the tough fights that you
can't avoid).
The reason why I mention this game is that there are quite some puzzles in it, which get harder as you proceed. Some of them are quite nifty, but also a lot of fun. The hardest puzzle is a puzzle that you can skip, but where you get 4 neat items if you do solve it. You can check it out on
Youtube where someone managed to do what I never accomplished. They are not all
that hard, but there are quite some that stand on a considerable level, and most of them are definitely more interesting than this.
There is also a dungeon in Lufia 2 which is basicly a price winning game. At the beginning of this magical dungeon, you have to part of all your weapons and items, and you start back at level 1. The dungeon consists of 99 floors, and you get stronger and obtain better weapons while going deeper. The first 10 floors have enemies that are quite easy, but the dungeon gets pretty tough as you advance, also because you can't save and barily heal, and because the dungeon is never the same as the previous time you played. If you die or quit, everything turns back to normal with regular levels and items, and you even get to keep special certain items you find in the cave. The dungeon isn't really a puzzle, but requires definitely a lot of tactical thinking, and also it gives of course a very rewarding feeling if you actually beat it since it is quite the challenge.
From all the adventure RPG's that I played for the SNES, Lufia 2 definitely makes my top three. It has a nice gameplay, funny dialogues, fun puzzles and a good story I think. A story that isn't as great as say, Baldur's Gate, but for such a SNES RPG it has some nice plottwists and is interesting and fun enough. I don't know if this is excactly the kind of game that you are looking for, but I can nonetheless recommend it to you as a side thing (if you have a Super Nintendo). For anyone who is into these kind of 90's manga SNES adventure RPG's, and especially for everyone who liked Chrono Trigger, I can very much recommend Lufia 2.