So I discovered Fallout thanks to GOG and it's been really really fun. I can't wait to dig into the second one, but I really don't want to until I've gone as far as possible in the first.
The thing is, I think I've broken something. For starters, when I got really lost at one point, I did some reading at NMA. There was something about a girl getting kidnapped in Shady Sands, which I never heard about (never turned up in my Status thingy either). I did destroy the radscorpion cave, however, and felt quite pleased about it.
And so far, I've done a bunch of things in Junktown, I killed an assassin and I ended up killing the owner of the casino. I've also done a handful of missions in the Hub. I've done the Thief Guild steal the necklace thing (apparently it's a worthless necklace! I hold onto it for keepsakes), and I decided to be naughty and I did a couple of really well paying jobs for the guy in the Casino, so the merchant and his wife are also dead.
Next thing I know, I ask the gun runner for more punch-y weapons and he directs me to the BoS. I turn up at their door, and one of the guards tells me I have to retrieve something incredibly vague from an undetermined location somewhere south. After wasting time looking for it and failing, I loaded the save game and I lockpicked the door with an electronic lockpick, alerting neither guard (so amazing job there, guys). And all of a sudden everyone's referring to me as an initiate in the BoS - I've even saved the initiate in the Hub for Taurus. But whenever I go back out again and talk to the guards, he asks me if I got the thing he wants me to go fetch.
And I'm really, really lost.
EDIT: Should have specified Fallout 1 in the title, sorry!

I've seen some people complain that they were shot by the brotherhood guards if they tried to pick the lock on the door.
I've also seen it suggested that if your Karma is high enough, you can pick the lock without a reaction from the guards. I'm not sure how high adricv's Karma would be after doing the killings in The Hub.
It may be that once you accept The Glow mission, you cease to be a "threat" to the guards, so you can therefore get away with breaking in. Everyone else in the Brotherhood base is set up to assume that only an Initiate can get in, so they treat you like that if you get off the elevator.
I wonder what happens if you kill both guards before you pick the lock?
By the way, the main reason to complete the quest is for the loot, plus some interesting but not vital plot clues.

The location you're looking for is The Glow. It's on the southeast of the world map.
You'll need two ropes to get in, IIRC. Also, since it was a nuclear ground-zero you'd better have a couple doses of Rad-X and Rad-Away on you.