FFX's minigame mostly annoyed me :(
Also ACF was a lot less puzzley than the original WA1 from what I remember. Basically ACF is weird and I would avoid it. They add a lot, but they take away about as much as they add, and I'm not sure they new additions matter, because some of them are based out of really questionable design decisions from WA2 and 3.
Basically you should try looking for Zelda-like games. They generally have that kind of stuff. Alundra was mentioned as was Ookami. Landstalker for the Sega Genesis was pretty sweet too although some people hate it (except they don't count because seriously they're just haters and haters gonna hate, you know?)
I don't know how puzzley and minigamey Valkyrie Profile really is but I think you'd probably like it based on your interests.
Does anyone else wish CT had more minigames and puzzles throughout, a la the millennial fair?
Majorly Your Mileage May Vary, but Omikron is sort of neat. Tho i'd recommend the PC version because it has the stupidest fucking save system and you can find various hack and cheats to deal with it on the PC.
Puzzle Quest might work although I doubt that's the kind of puzzles you're talking about :P Also the randomness started getting to me in that. SPEAKING of DS games, though, Rocket Slime is short but pretty nifty
Ultima games don't have a lot of minigames but they are pretty puzzle-oriented. Especially 6 and 7, although really from 4 onwards a huge part of the games involved a lot of clue gathering and solving NPC-oriented puzzles.
Also Quest for Glory 2 VGA which is an adventure/RPG hybrid and pretty much one of the best games I've ever played and also freeware. There are little minigames to raise your stats, a nice battle system, lots of puzzles from being part adventure game (and different character classes have access to different solutions which is *awesome*). http://www.agdinteractive.com/games/qfg2/
BAT 2: The Koshan Conspiray would also probably work although I never got anywhere in it. I know it's basically an adventure game with lots of minigames and RPGish elements.
Space Rangers 2: Reboot. LESS RPGish, but it still has more stats than your typical space trader. Not a lot of puzzles. TONS of minigames, though. Text adventure missions, RTS missions, and arcade game-y missions. And the main space trader portion of the game has a ton of things going on.
You'd probably also dig Star Control 2: The Ur-Quan Masters. Also freeware. Less RPGish, more adventure-ish, lots of puzzles, sort of minigamish. Read up about the time limit though. And don't use the remixed music or the 3DO music, they suck. http://sc2.sourceforge.net/
There's also God of Thunder http://www.adeptsoftware.com/got/
(totally one foxy brachiosaur)