To simply put, "because Voldemort likes grandeur", as stated by Dumbledore to Harry
The same reason he wouldn't make his horcruxes ordinary objects that would blend into the environment and would be practically impossible to detect, such as empty potion bottles or grains of sand on the beach
A cave full of inferi and a bunch of dark magic protecting the locket, with the locket being buried deep in a potion that can only be drunk through a magical flask, inside a cave which symbolised one of the first instances of him showing his magical superiority over muggles seems much grander than just hiding it using a spell that makes it undetectable to anyone else. Furthermore, even if he did use the Fidelius Charm, it might be possible for someone like Dumbledore to detect where Voldemort hid it, even if he couldn't actually find it. In the last book while Harry, Ron and Hermione are on the run, Voldemort's followers know where the House of Black was, even if they could not go in themselves to catch him.
Similarly we can understand why he would choose the other hiding places for his horcruxes. Let's go through them one by one:
- Ravenclaw's diadem at Hogwarts Castle: It can't get any grander than that.
- Hufflepuff's cup at Gringotts : We don't know for sure whether he chose Gringotts for the cup, but he entrusted it to Bellatrix so we can assume that he knew she would chose a location worthy of such a valuable object. Or he might have just told her to keep it in a nice safe place, and Gringotts might be the nicest safest place she could think of, which also holds her family's fortunes gathered through generations (why she didn't hide it using the Fidelius Charm is anybody's guess, but then again, she probably did not know how valuable an item it was, just like Malfoy didn't. She just knew Voldemort told her to keep it in a safe place, and she did)
- The diary : Similar to Hufflepuff's cup he had entrusted the diary to one of his most loyal followers. Too bad Malfoy tried to use it for his own gain once he thought Voldemort had gone forever, but that's not Voldemort's fault.
- Peverrel Ring in the Gaunt House: This one does not hold much grandeur I admit, but it was important to Voldemort, kind of like the diary was. The diary was not a historical object, yet Voldemort used it as one of his horcruxes because of it's personal value to him. In a similar way, he used the Gaunt House to hold the ring because the place had a personal value for him. It was the house of his ancestors, a pureblood line descended from Slytherin.
The remaining parts of his soul are in the snake, Harry and Voldemort himself, but I think it is obvious why they aren't hidden in grand locations.