Same issue, even after turning down the recommended settings. I have tried turning off (not just putting into standby, but full restart) my Xbox as well as reinstalling the game (took over 6 hours to clear data, redownload and reinstall). I am at the part after "meeting" Johnny (trying to avoid spoilers). Before the reinstall, I made it to the street, tried calling the car, game crashed. After, realized I can't do that, read the text about the car, game crashed. Ignored the car stuff, got to the road, game crashed.
I tried to do an earlier save file (thinking maybe the file was corrupt or something) and redid the mission before meeting Jonny, but then it crashed in the apartment. So that is when I reinstalled the game. Now, it crashes on load for the apartment, and going to most earlier saves causes the game to crash after V meets Jonny. It didn't start happening until after the new patch (1.04). Prior to that, the game would hang up for about 10-20 seconds at random points, then continue as normal.