I bought the Fallout 3 GOTY edition and installed it and then moded it a little. After playing it for a few hours and arriving at Rivet City my game crashes whenever I leave Rivet City into the area surrounding it. As long as I remain in Rivet City the game runs fine. What is interesting is that this is not the first time I went to Rivet City, its like the third, and the two times before this I could leave with no problems, and I cant think of anything that changed between these trips to Rivet City. I have not added any mods or deleted any, and I cant think of anything else that might have changed. Could anyone help me with this problem? Thanks.

Let me guess, you're using the Unofficial Patches? If so, look for the fixed version of the Broken Steel patch, there's problems with the original one when it comes to Rivet City. The issue is in the Autosave, the game will crash when it tries to save your game. If you disable that and move a short ways from the ship things will work normally again.

So do I add the Brotherhood of Steel patch and that will fix it? Or do I disable autosave for a while? Or both?

There's a fixed version of the Broken Steel patch available somewhere on the Nexus. Just get that one and replace the original with it. I haven't had any problems at Rivet City since I did that, but before I had to disable Auto-Save at that point or get an instant CTD as soon as I left the ship.