Unique boss fights: Boss fights that don't resort to tank and spank, that require knowledge and use of patterns and game mechanics. Fights where position matters, and certain types equipment are mandatory/extremely useful

Unique dungeons: Dungeons that have various gimmicks or different types of gameplay. Examples would be the magnet cave in FFIV, where you're not allowed to wear metal equipment, or the giant's cave in FFIII, where you're forced into the mini status, and all of the enemies are huge versions of regular enemies. Dungeons that make use of teleport mazes, puzzle solving, and a variety of other things

More class specific content: Quests that cater to evolving, equipping, or even using classes, such as getting the summons for SMN in XI. Memorable quests that are vital in making your character, well, your character

Things that reward exploration: A redesigned world that interesting to see, with unique areas that have great views. Reward players for exploring by putting high grade gathering points within hidden away areas, and even having treasure chests occasional spawn in unique spots that could occasionally have nifty items or equipment.

Those are the things I would like to see the most