Re: Aggie here, visiting Columbia next week
I'll let someone else chime in on food options - nothing incredibly special, but some pretty decent spots close to where you'll be staying.
As for runs - one of my favorites use to be zigging and zagging around the campus with lots of loops around The Horseshoe (old/main part of campus) thrown in. I've been to College Station - you'll be pleased how much better it looks ;)
Also, try the trails along either side of the Congaree River, accessible just down Gervais. The sections on the far bank are linked better. My single favorite running spot in the area is Susquicentennial Park - but that's a decent cab ride away.
"A nation that makes a great distinction between its scholars and its warriors will have its laws made by cowards and its wars fought by fools." - Thucydides