Minesweeper! ...Ahem, sorry. I just rather enjoy playing Minesweeper during my free time now and than.
But to the topic title itself, yeah I think it'd be neat if there were some more puzzle related stuff. As for the 3 suggested things, hmm~
Hint/Clues are kinda neat. Sometimes it's just nice to use some intuition and figure something out on your own, plus if you get stuck you can ask another player for a hint/guidance.
Map-based Puzzles though. Eh, I think they're hit or miss. Gilead's reverse symbol order thing to reach the Mana Elemental is kinda annoying, but I rather enjoyed J6's Hyperium, what with the Turrets and how you could collaborate with other players to temporary disable them (although most folks just chug an evasive potion or use a dodge boosting move and run past), open his secret shop through a combination of dials, and could pickpocket J6 to enter his VR room. Hyperium probably isn't the best example of just map based stuff though, since the J6 saga is also filled with hints and mini games. Great example of an very good story with puzzle elements though.
Minigames... As long as they're somewhat enjoyable to get through I don't mind em'. Some of the previous in game ones have been kinda iffy though. Two different Simon Says like games exist in both the Ember Isle and Brightoak stories, and they were a bit of an unpleasant annoyance to get through.
Overall though, I think I'm more in favor of Hints/Clues, but as long as the map based puzzles and minigames are well done/executed, they can be great additions as well.