At first I thought it was because I hadn't gone anywhere and had just waited in the place I was after I patched, but then after moving to a new location, I'm getting the same issue. The game just freezes at some point during the wait screen and I have to hard boot the 360 to get it working again.
It may be worth noting that I'm waiting in 24 hour blocks to see if Boone shows up now that the game has been patched. Or at least thats what I'm trying to do.
Have you tried holding the Right Bumper, Left Bumper, and the X button simultaneously while the game is booting? Doing that clears the FNV cache without removing patches.
What locations is it happening?