Fallout 3 Crashes when trying to exit Vault 101?

My best guess would be to try and alter some settings in the game.
Go to the installationfolder of your game and locate the file FalloutPrefs.ini this file might be located in the submap Fallout3. Open this file with a texteditor such as notepad and find the following line and change its value bDoHighDynamicRange=0 to bDoHighDynamicRange=1

Try to start the game and exit the vault. If this doesn't work, you could try some other settings.
For this you'll need to find the file Fallout_default.ini also located in the gamefolder.
Find the following values and change them:
Change bUseThreadedAI=0 to bUseThreadedAI=1
Change iNumHWThreads=2 to iNumHWThreads=1

If either of these options don't exist, you should add them in the [General] block of settings.

What this will do:
bDoHighDynamicRange turns on HDR.
bUseThreadedAI determines if actors' behavior scripts can be split into multiple threads. This might improve performance*
iNumHWThreads controls the number of threads the game uses in general. *

*Link for more information > Fallout.ini (Gamebryo)