I would love to see a parking lot food cart court happen, but wonder where a prime location/time would be. Parking lots around the city are in heavy use between 8am and 5pm M-F, and arguably the weekday lunch crowd is when the strongest customer demand is likely to be. It might be hard to find a parking lot owner (private or city owned) willing to give up spaces during peak hours for this kind of setup.
I do think that the Columbus Commons & Pearl Alley ideas might be a better fit. I've always thought that some of the other downtown alleys are a bit wasted as well, and it probably wouldn't be too hard to get a closure permit if this is attempted as a one-off event to start with.
Maybe the dead-end alley portion of Elm Street (between Gay and Long) just east of High Street could work? Essentially, close off Elm from Wall to High and line it with trucks and carts and make it a little pedestrian space.
Link: http://maps.google.com/maps?client=safari&q=columbus,+oh&oe=UTF-8&ie=UTF8&hq=&hnear=Columbus,+Franklin,+Ohio&gl=us&ei=MI3dS67wEYSqNuy5kLwH&ved=0CBAQ8gEwAA&ll=39.964145,-83.001934&spn=0.002545,0.004034&z=18&layer=c&cbll=39.964236,-83.001953&panoid=1N5yMEB9n0IYspr7nsleIQ&cbp=12,98.74,,0,15.29
You'd get a lot of visibility from High in that location, and it's still pretty much in the middle of Downtown and accessible to most of the office crowd.
Of course, if you're wanting to do this on a weekend, then the options open up quite a bit. Could probably stick it just about anywhere. ;)