You would never know that Link's Awakening is based on a game from the early 90s. Nintendo has done a great job of updating the graphics and the music from the original, as well as providing extra (although largely unnecessary) content to the game to make it more palatable for the modern player. As a caveat, I never played the original, but I have played almost every other Zelda game ever made, so I can't comment on how this game is compared to the original. Instead, I'm just basing my comments on my enjoyment of this game in this format for the first time.
The graphics in this game are some of my favorite in the entire series. This might be the most adorable Link ever created. I constantly looked at the screen and just smiled because my character was just so cute, or something else that was going on in the game was endearing. Everything kind of looks like it was made for kids, but is still beautiful for adults. The soundtrack is also great and includes orchestral renditions of many Zelda songs.
The highlight of this game for me was how weird it was. It is the only Zelda game that openly references other Nintendo titles. You have sections where you literally are dodging fireballs and stomping goombas, and these are nestled right in the middle of dungeons and always brought a smile to my face. There is a lady with a Chomp pet, and one of the sidequests (maybe it's required, unsure) that lets you give it a bow which is wears for the rest of the game. It integrates all of the fun Zelda questing (dungeons/puzzles/minigames) while incorporating a fun fetch quest that lasts almost the entire game and has you traversing the map to switch out items between everyone on the island. The story is also surprisingly dark. I usually don't give a f*** about the plot in a Zelda game, but when they talked about how this entire island isn't real and waking up the Wind FIsh will essentially kill everyone, I was actively rooting against myself to beat the game.
The dungeon designs are interesting and varied, and I never got so stuck that I felt frustrated in them (with the exception of the dumb decision to make some puzzles like the chess pieces just trial and error) and the boss battles were all fun, if not especially difficult. The world map fills out as you travel, and when you acquire new items you can go to new places and acquire new heart pieces and other secrets as you progress. While obviously not groundbreaking, I always enjoyed finding a new hidden secret in an area I had explored hours earlier.
The part of the game that frustrated me was the overworld. It was never quite clear where to go, even with the owl giving you extremely vague clues. Saying to go to the "signpost puzzle" means absolutely nothing when you haven't been able to access that area of the map until now. There were several times outside of dungeons where I was completely unsure of where to go, and while there is a fast-travel system (which is great by the way) between different parts of the map, you may find yourself traversing the same areas multiple times just trying to figure out where tf you're supposed to go. Other Zelda games have given much better instructions of where you need to be headed, and this is the worst I've seen in one where your directions are just unclear and frustrating.
Overall, I really enjoyed my 18 or so hours with this game, and I hope Nintendo re-makes some of its other Zelda classics so that we can also enjoy them again.