With Pokémon I've always saved my game in a Pokémon Center out of habit. I don't know why, but I've just always done it.
Having save points in games aren't necessarily a bad thing in certain games. They create a spot to strive towards, and usually are handled well within reason. Some games do not use them well and are a pain to follow up with. For example on how they're handled well and poorly we'll look at the Dead Space series:
Dead Space is a third person science fiction horror game based on the cracker class starship the USG Ishimura. Throughout the game, you fight your way across the ship, restoring systems, fighting off enemies, the biological hazards, and even the mechanical hazards. What makes the game great in terms of saving functionality is that the saving stations are located throughout the game in convenient places that do not warrant you to track back four or three hours just to reach where you left off. In addition to handling the manual save it also offers an autosave feature which is quite handy as well. Dead Space 2 utilizes the same formula for saving: fight your way here and there and you'll likely find yourself face to face with a save station.
Dead Space 3 on the other hand is a pile of regurgitated trash so putrid and so foul that it even causes Muk and Grimer to flee in terror. There was no manual save in Dead Space 3, and there was no option to hold your place besides an autosave that didn't even function properly, and you would find yourself 8 leagues backward from where you were from where you left off. Example: you fight your way through a vicious area filled with creepy critters. You make it to the next area and you're out of ammo and it autosaves. Great, time to take a break. You come back a day later to find yourself in the room you once cleared of hostiles and you have no ammo. Dead Space 3's autosaves saves the state of your ammunition more accurately than your position.
So in short, manual saves are more effective than autosaves. So I believe that Pokémon should never stray from the time proven formula of saving wherever you may be (perhaps they could disable saving in the Elite Four to provide added difficulty). I also enjoy the fact that the saving function has been much improved with the latest editions of the games. pretty soon they'll have it to the point where it'll save nigh instantaneously.