I have been running the game with 0 errors until I got to this area shown in this screen shot. This is in the Hub, right when you walk Old Town, there is this room, with guys that starting attacking me right away.
If I wait too long at that screen, or if I do ANY action, this error will occur.
I really could use some help, or advice. Thanks in advance.

I went into it (luckily enough I had just reached the hub :)) and got no problems at all with that place, so it's not the game at least.
Do you have all those programs running "Xfire" for instance?
If I were you I'd quit that and other programs you don't need, it might be one of them using that memory address and therefore FO crashes. (I'm not sure if it'll help, but it might be worth a shot)
Otherwise it might be a slighly faulty memory chip, have any mates you can borrow one from or do you have more than one in the box? (if so - more than one - try switching their positions and see if that helps, or try one at a time in the first mem. slot, you might need to go into BIOS with this though, depending on whether it's set to notice such changes automatically or not)

I will try the closing some of my programs first, and I do have Xfire running. Hopefully, that is just the problem.
I am not certain what you mean by memory chip, but if you are talking about my RAM, that is certainly not the problem. I can run modern games with it, without errors, but I will try switching the slots if closing some programs doesn't help.

Look at the worldmap before you reinstall, that way you can check it pretty fast, just put the cursor around where the hub is and click there to run towards it. (if you get a random encounter just start running towards the edge and you're likely to make it out alive)
This way you won't have to get directions and all for the hub before going towards it at least.

I seriously doubt it's RAM. Like I said, that same kind of error is what you always get when Fallout bugs out. I've gotten it myself occasionally, just randomly. But if you keep getting it in the same place like that, it's a Fallout bug.
Patching tends to reduce the game-stopping crashes, but Fallout is still, after all these years, buggy.

1. do you use any mods?
2. they attack you because you have your gun equipped, move it to your inventory and they (usually) won't attack you.
3. If the error doesn't appear after entering without a weapon, it looks like you've figured out specifically what the issue is.
4. Do you usually suffer from extra "r's" in your errors?

Heh, didn't even noticed I misspelled it.
No mods, besides the patches recommended above. And it isn't the being attacked I am worried about.
Anyway, I did use those patches that were recommend, and I only had one crash so far, and it isn't repeated in the same spot, and it doesn't happen repeatedly.