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Guess Who I Saw Today - Dr. Henry
You can start this quest by talking to Dr. Henry in Jacobstown. This old ski resort has become a refuge for super mutants. You can find it at the end of the road to the northwest of New Vegas. Dr. Henry is inside the main lodge in the side room that functions as their hospital. Go inside and talk to him to learn about their problem with the nightkin.
For starters, you'll need to help him look around Charleston Cave to figure out why the nightstalkers are suddenly projecting stealth fields (and how that might help him cure the nightkin). If you want, you can recruit Lily now. You don't have to though, it's just an option. You can pick her up as a companion at any point in the future.
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Guess Who I Saw Today - Charleston Cave
Charleston Cave is just a short walk away from Jacobstown. You will need to walk out the main gate and then follow the path along the palisade and then up into the marked cave. By the way, you'll probably trigger "Unfriendly Persuasion" on your way out. You can do it now if you want.
This is actually fairly easy. Don't underestimate nightstalkers, since they can cause a fair bit of damage. Note that they do have stealth fields, so you'll want to shoot them at least once at a distant to disrupt the field. Melee weapons work fairly well too, since they'll have to rush you to attack. That said, make sure that you bring stimpaks with you if you plan to take that route. You will be bitten a few times if you try to fight at close range.
There is a bed in the first area though, so if you're not playing in hardcore mode you can just take a nap on your way out.
Walk forward into the cave and just watch out. Nightstalkers aren't exactly quiet, so their stealth fields aren't actually that helpful. Just shoot them when they attack you and keep your eyes open. Also bring a companion. If you miss something, they'll probably spot it. Since Lily is literally just outside, you don't have much of an excuse.
There are two paths to get there and the whole cave is just a big circle of tunnels. You can go downhill and through irradiated water, or just go straight forward through a cavern with multiple nightstalkers. Either way, you're looking for the big cavern with two bighorners and a dead nightkin. Examine the dead nightkin to find a chewed stealth boy on his body. Take it, and take his super sledge "Oh, Baby" even if you don't use melee weapons. It's incredibly valuable and very deadly.
Backtrack back to Dr. Henry and hand in the chewed stealth boy to complete this stage.
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Guess Who I Saw Today - The Experiment
Once you turn in the chewed stealth boy, you'll need to help him with the experiment. You can do your part by talking to Lily and asking if she still wants to do the experiment. She'll immediately agree and report to Dr. Henry. Talk to him to have him start the experiment. Just watch for a moment until he finishes.
Once he finishes, Keene will rush inside. You'll need to settle this one before you leave.
Keene wants to have the specifications for the Stealth Boy Mark II Prototype. Obviously Dr. Henry doesn't want to give him the specs due to the chaos that this could cause. It's up to you though.
If you have 80 points in Speech, you should be able to just talk him down. If you want to help the super mutants, this should also be the most beneficial.
If you don't want to give him the specs, and you say so, he'll attack. In my case, they actually went down in just a few swings of "Oh, Baby." The only real problem is that you need to be very careful to not hit any friendlies in the room. You might want to stick to VATS for the start of it and avoid fighting by the doorway.
If you don't want a fight, just hand over the plans and he'll walk away with some of his nightkin followers.
Talk to Dr. Henry at the end (you can get a briefing from Marcus too, but it's not necessary). Dr. Henry will note his problem and the future of the experiment. You can either have him continue the tests on Lily (you can still recruit her, since it's a long term test), say that it's too great of a risk or successfully convince him to just use Nightstalker brains with a massive 90 points in Science.