New settings. DS3 was just lazy with its environments: oh yay, more generic castles, cathedrals, caves, cathedrals, snowy towns, delapitated towns, cathedrals, ruins, cathedrals and did I also mention cathedrals? How about shuffling through the tight streets of middle ages Timbuktu? Or Mayan temples? Jungles? Indian palaces? This extends to all of gaming by the way, but especially to Souls.
More focus on character storylines. I don't need every character to show up in the most blatant locations, but even one or two questlines which every player would see to the end on their first playthrough would make a difference. Judging by how many people were sad over Solaire's storyline in DS1, imagine seeing that with multiple characters. And I don't only mean jackasses who only sit in one spot and occasionally serve as summons, I mean characters who are vital to the plot and whose backstory isn't relegated only to item descriptions. Siegmeyer's questline in DS1 is one of the saddest in the series, yet its last three stages (him being in Blighttown, then in Izalith, and finally in Ash Lake) are nigh impossible to discover without a wiki. I want to feel sad to see these characters die, and not just because they've helped me in gameplay terms, but also because I care about them as a character and wish to see them succeed.
More oomph in the combat. The system is quite robust as it already is, but with little touches it could be even more satisfying. Imagine if when you managed to hit a zombie's head with a mace the body doesn't just fall limp, but you actually hear the sound of and see the skull cracking open! Dismemberment, visible damage on the models, gore that doesn't just disappear, changing animations and AI patterns on enemies depending on where they're injured... there's so much you can do!
Environment affecting gameplay more. For example, your stamina would deplete faster in a lava or fire area, requiring you to switch up your tactics. Going into water deep enough would increase your equipment load for a period of time (I haven't seen any game other than Dragon's Dogma do this, yet it adds so much to the immersion). Casting fire spells would weaken ice-based enemies. Casting lightning around metal surfaces would make it conduct, possibly damaging more enemies.
Better character mobility, or for the love of christ construct the world in a way that doesn't make me constantly go "Why can't I just go there?". Dark Souls 2 would essentially lose 2/3 of its length if your character was simply able to move over a small pile of rubble. You could skip half of the Catacombs in DS1 if your character could just crawl through a very wide gap in the rock. That kind of things breaks immersion super hard.
For the love of God, stop having the enemies being able to hit me through 20 ft of solid rock while my weapon bounces off it!
Follow DS1 in the amount of hidden nooks and crannies you can find, and have it be worth it. I only last week discovered how you find the Great Magic Barrier miracle in DS1, and I was staggered that a game I've beaten around 8 times still holds new secrets for me to find.
Make new magic types, or at least make the ones we have now more distinct from one another. Now there's rather little difference between Fireball, Lightning Spear or Great Soul Arrow aside from projectile speed, casting time and damage. Perhaps fire damage would freak out enemies in darkness, like the torch did in Old Yharnam in Bloodborne. Sudden lightning spells could blind and stun enemies. Magic could perhaps disorient enemies. Imagine introducing bending-style magic where you use the environment to your advantage! So many possibilities!
Use the horror elements more! New Londo Ruins, Tomb of the Giants, and the Upper Cathedral in Bloodborne are all incredibly atmospheric, terrifying locations. Souls already has sublime sound design, and it's one of the most vital elements of horror. Holy shit, imagine a Souls game crossed with Silent Hill's sound design!