What I long for most: the 1e AD&D Bard.
I can understand longing for it more than playing it, since it took so long to qualify. ;P
The intricate Non-lethal and Weaponless Combat Procedures.
OMG, someone actually used those! ?!
The Construction and Siege system and how everything in the 1e AD&D economy logically fit.
1e's assumed 'gold rush economy' really didn't make oodles of sense. I mean, on a basic level, it's fine, prices assume adventurers coming out of the dungeon with bags of holding full of coin - or speculators blowing their life savings on gear to go into the dungeon, but everything up to constructing castles running on those assumptions, not so much. The 'economies' of 3e & 4e weren't any more sensical in a broader-world way, but they were more workable w/in the context of a PC-centric campaign, and they could be assumed to make sense, like the gold-rush economy, in the limited context of adventuring, and, in 4e, of paragon & epic 'economies' that just operated on an entirely different scale.
What I love about 5e: Combat is fast. I've been stuck in 1e AD&D combats that last hundreds of rounds.
Amusing. 5e 'fast combat' design was aiming for an AD&D experience.
AD&D experiences varied.
What I like/love about 1e: That classic feeling -- something beyond just nostalgia. The feeling of adventure from the point of view of children riding their dirt bikes into unknown, uncharted territory. The Goonies Effect. There's a reason that Speilberg and D&D are making a comeback and it's not just nostalgia: it's the Great Unknown. 5e doesn't capture that and it never will -- it's just resold dreams.
Sounds like nostalgia, to me.

Really nice nostalgia: it's good to have had experiences like that to hearken back /too/. Worth appreciating, enjoying, & celebrating.
I will laud any approach to make modern systems feel more like those from days of yore which make me feel all warm, fuzzy and nostalgiac.
Y'know, part of what makes me nostalgic for gaming in the early 80s isn't the mechanics of the game, it's the presentation. Staple-bound magazine format rule books, amateurish line art & editing - a step or two above a 70s 'zine, but still clearly a labor of love more than a commercial enterprise.
Nobody cared about balance, terms such as DPS and AoO did not exist, ASIs too.
We did have 'balance' - in concept, EGG used the word himself, enough, in the DMG - and some of us did care about it. And we had hot-button debates (in super-slow-motion of letters to Out on a Limb, compared to forums or - gak, Twitter), 'realism' was a hot one (and still is, though most folks banging that drum wouldn't call it that anymore), and dwarven women's beards, for some reason... ;P
If you're going to do that, then you're wasting your time starting with 5e and trying to strip away all the "new school" elements. You'd be a lot better off with AD&D, or an OSR retroclone like Swords & Wizardry.
Sure, if the entirety of the experience and one's emotional investment in it were confined to the table, it'd just be a matter of finding the best game for you & your buddies to get what they want out of. If you wanted nostalgia, it'd be re-playing that old game from back in the day, or, if you want it tweaked & improved, maybe a clone.
But that's not all there is, there's a community, and there's a sense of validation that comes from being even nominally on the same page as the current 'state of the art.' 5e delivers that fuller sense of the experience, not just connecting to the game you played back in the day, but connecting /that/ to the current incarnation of the game.