The best dungeons in the series prop up an otherwise unremarkable game
Any discussion about the quality of Twilight Princess inevitably boils down to a single question. How much do you care about the dungeons in a Zelda game? Are they the most important thing to you by far? If so, you will find Twilight Princess to be a deeply satisfying experience.
It cannot be overstated how great the dungeon design in Twilight Princess is, especially coming hot on the heels of Wind Waker, which has both the fewest and the worst dungeons of all the 3D Zelda games. The dungeons in Twilight Princess make Wind Waker look like absolute amateur hour in comparison. They made you feel, upon revisiting Ocarina of Time and Majora's Mask, that the intervening years were not wasted, that Nintendo had actually learned something and were moving in a forward direction of iterative improvement. In an otherwise formulaic series afraid to take risks this was incredibly important. Nobody wants to play a game with a tired and familiar formula that isn't even an improvement over past titles.
Unfortunately those improvements are marred somewhat by the fact that the dungeons are the only thing in the game that stands out. Almost everything you do outside of a dungeon is unmemorable at best, tedious and frustrating at worst. From hunting bugs as Wolf Link over and over and over again in the opening third of the game to possibly the worst escort mission in all of video games, the overworld is something you wish desperately to get away from at every turn. This is perfectly codified by the game's opening hours, which has you performing mundane chores, completing frustrating mini games, and buttoning through mountains of oppressively boring dialogue before you ever get to see the inside of a dungeon. Nintendo seems to have placed a far greater focus on story this time around. They want to set the scene, build up tension, make you care about these characters and Link's quiet little village and quiet little life and the evil that disrupts it--and it couldn't fall any flatter. If ever you needed proof that Nintendo are great game designers and terrible storytellers, look no further than Twilight Princess, the most 'movie-like' Zelda game.
It's not all bad, though. Despite being horrible storytellers, Nintendo has always had a knack for creating interesting, quirky characters, and there's still some of that, when the game deigns to stop taking itself so seriously and isn't shoving exposition and hackneyed character drama down your throat. Midna is a great new addition, full of sass and constantly insulting Link with hilarious quips. I'll take her over Navi any day of the week. The main, non-ganon antagonist, Zant, is in turns goofy and legitimately creepy. Skull kid with a sense of humor, if you will. You will cross paths with a weird little bird creature throughout the game who's...kind of disgusting to look at, only to later find out that their species live in one of the late game dungeons. I couldn't help but laugh when I spent the entire game thinking how weird and stupid looking this little creature was, only to be confronted with way more of them. It's not unlike encountering the primordial serpent Frampt in Dark Souls and then seeing a bunch more primordial serpents in one of the ending cutscenes. All you can do is laugh at that ridiculous imagery.
One of the things I found most memorable, and which most people probably didn't enjoy (if they engaged with it at all) is the cave of trials. This is a 50-level, pagoda-style combat trial with checkpoints every ten levels that is entirely optional. The reason I enjoyed this so much is two-fold. For one, Twilight Princess has the best combat of any Zelda game to date. Hidden moves compliment the standard, simplistic slash/block/jumping attack combat that all past Zeldas had. You can finish off enemies on the ground, bash them with your shield to stun and do a special followup attack, parry, and roll around to an enemy's back and do a rising slash. Unfortunately there are very few encounters in the standard game that are challenging enough to make these extra moves feel particularly necessary. The cave of trials, on the other hand, gets fairly challenging, and I enjoyed getting to put those new moves to the test.
Twilight Princess may not be the best Zelda game. With games like Ocarina and Majora still holding up fairly well, and with Breath of the Wild being a wild reinvention of the series that's arguably the best ever, it's not even a serious part of the discussion. It does, however, deserve recognition for the improvements they made to the combat and for being the high point of dungeon design in a series known for its dungeons. For me, that's enough to place it above Wind Waker, however slightly.