Well, for what it's worth and what I've read, Jesus Would Walk, most likely. And for this supposition, I take a number of points to support this.
1) He always walked before. Walked across the dead sea, walked to Jerusalem, walked to Golgotha. Walk Walk Walk. Dude had a heck of a figure.
Everywhere is walking distance if you have the time.
2) Walking is a social activity, as is taking mass transit. J.C. was all about interaction and getting to know the 'hood. Meeting chicks at wells, shooting the breeze on some mount somewhere. He liked to talk to people. Cars close you off from other people, 'cuz it's hard to have a conversation with the guy in the Trans-Am next to you at 75mph. 'Course, he could carpool..
3) Ecology. If your dad built a house, would you walk around on the shag rug with muddy sneakers on? I'd hope not. And so the J Man probably takes the same opinion of the world. His creator built the place, and now he's gonna pollute the atmosphere all to.. the lower kingdom? Not likely. He's probably all about recycling, too.
This is not to say that Jesus doesn't own a car, he just doesn't drive it much. I've seen it, it's a bitchin' Jeep CJ with a lift. Nice.