Does fallout new vegas have to be saved on a hard drive or can it just be saved in the console?

Depends if your console has built in memory. You can't save it on any of the old 360s without a memory card/usb/hd.

ya my xbox has built in memory

If playing on an Xbox, then you can either install the game to the hard drive or you can run the game from the disk. I prefer to install the game though, faster load times, quieter. And you dont want to install to a USB drive, it would be pretty slow.