I'm not sure I understand the question. Has anyone played DnD in a Fallout/Metro/S.T.A.L.K.E.R. setting? Or a post-apocalyptic PnP in general?
I'm not sure if DnD adapted to Fallout would even work. You have post-apocalyptic PnP systems, but DnD is just different. It's fantasy, and designed for fantasy RPG. Spells, Skills, Races, Classes, Weapons all reflect that. You'd have to a whole lot of homebrewing and houseruling to make DnD system (5E especially) work for an SF post-apocalyptic setting, and that takes time and effort. So much effort that it's probably better to just look online for an already existing PA system and just change it up a bit. But that would still take work. And if you're a newbie at DMing, it could be a challenge.
But you asked for a quest, so this is the basic blueprint that I use when DMing. It's useful for basically any setting, fantasy, PA or otherwise. I'll write this very noob-friendly, as someone else taught me the same thing long ago.
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Design your initial village/small town. It should be small, because bigger settlements work under different rules and are more complex. Small in a sense of "everybody knows everybody".
Your reluctant heroes arrive in this town, or they meet here. Maybe it's a stop on fairly-frequented road, such as one leading up to a bigger city. Maybe you don't need an explanation, they just met in a tavern/bar here. Whatever. Player introduction is the most boring part of any game.
Make sure your town has a basic tavern, at least one figure of importance (such as a town mayor), and one shop/blacksmith.
In any case, heroes learn that the town is in desperate situation. A child/girl/many people have gone missing/been kidnapped/raped/killed by a local band of goblins/kobolds/orc/raiders etc. Since it's a shitty little town, they have no real chance at organizing actual defense or assault the villains' hiding place, so they ask the players to do it for them. This part here is important, as it sets a tone for the game.
You wanna go grimdark? Make it a young girl who was raped and mutilated and everybody was shit-scared because of that. You wanna go a bit more "regular"? Well, the aforementioned girl was *just* kidnapped (in my experience, since most players tend to be male, this "damsel in distress" scenario works well, even if it is cliche as fuck).
To incentivise the players, make sure that the mayor/shopkeeper/whoever promises to give the players a reward for a job well done - money usually, but maybe a weapon or some other curio can be handy as well. A free night and meal at the tavern. Hookers on the house. That sort of stuff.
Players are vaguely informed of the goblins/raiders' location, and they set off.
That's basically how you kickstart your first dungeon adventure.
On the road to the dungeon they should probably have at least one rest stop with an arbitrary random encounter - attacked by wild dogs, for instance. Newbie players will quickly catch on the idea that no place out there is safe, and also learn how encounters in wilderness work. Otherwise, it will provide that first streak of excitement and danger.
Now, on to the dungeon itself. If you are playing a PA setting, I guess your "dungeon" can be anything from an abandoned office building, factory, to a decrepit laboratory/underground shelter/Vault that raiders have taken over. Make sure you don't overpopulate the place, because early levels can be a bitch, and players hate when you kill their characters during the first session. Well, they hate it even more when you kill their characters during the 15th session, but you catch my drift.
Make sure you don't overpopulate your dungeon, but still make it a challenge. At early levels, it's really all about placing your enemies well. 10 goons in a confined room with no exit for players can be deadly - 15 goons split into smaller groups set around various points in the dungeon can be a fun challenge.
This is the biggest issue for newbie DMs, really. Balancing your challenge so that your players don't feel it's unfair. Fudging die rolls is a valid method, but players hate it when they realize DM is letting them down *too* easily.
Anyway, aside from enemies, maybe you'd maybe want to place a trap somewhere. Something simple that won't outright kill anybody, but will teach them how they should handle traps. But don't overdo it. Trust me, if you place a killer trap on the start, players will get paranoid for the rest of the session(s).
(I personally rarely place a trap on the first dungeon. I think it's too much most of the time, but suit yourself).
You also want to "enrichen" the dungeon with some loot. Nothing OP, but a good weapon here and some cache there works. Add ammo if you're going SF/PA. Maybe some random stuff that can be sold back to the shopkeeper in the town. Whatever suits your tastes, but make sure it doesn't make characters OP/too rich. And don't give stuff for everybody. Some DMs like to make sure that every single character gets something out of the dungeon that isn't just money - I disprove of this, you're just spoiling the players and they'll get disappointed once you start cutting down on the loot later on (while you want to go the different direction, from less to more).
So once the players murder everybody - or maybe they capture a prisoner? - they free the kidnapped NPC, or avenge their death. Back to the village, they receive the reward etc.
All of this should take...dunno, 4-5 hours max. Maybe more, maybe less. I'm partial to shorter sessions as opposed to all-nighters.
If you're too lazy to read all of this, here's a neat video that sums it up way better than me:
This dude offers great advice on DMing, you can watch the whole playlist. A very long playlist. But worth it.
Some other tips from me...
Depending on your story preferences, maybe you wanna place a McGuffin in the starting dungeon - such as, I dunno, some holodisk that needs to be decripted, or a mysterious artifact that they'll want to figure out. This gives a plot hook for players to go further - go to another town, look for an NPC who can help them, or get robbed of the said item and need to get it back and so on. It's all basic, cliche stuff, but it works very well. And if you've got a penchant for flowery language and know how to set the tone and atmosphere well, players will get absorbed regardless of how tropey your quest is.
Initial quests in general tend to be like this. Just look at 90% of cRPGs out there. Most early level stuff is samey from a mechanical and quest design standpoint.
Once you get a solid foothold on your story and characters, you will branch out, start designing the world and have a clearer picture. My only advice in this regard is not to overthink it - make some central conflict, tension in the background of the world (think NCR - Legion in FNV), but don't force it on the players. Not too early at least.
And be aware that whatever you design, your players will figure out a way to fuck it up. It's just the nature of the game. Adapt to what happens.
Maybe your players will come to conflict with the town's mayor because they felt underpaid? Maybe they're a villainous gang and decide to unite with raiders and attack the town? Maybe they'll just say "fuck this" and go to the wilderness to explore and look for a different town?
Instances like these are rare, but they happen, so you should try to respond as organically as possible.
