If you will have a car, try to get to Skillet in German Village for breakfast. A little on the high side for a college budget, but really good (about $12-15).
Refectory is near campus to the north and is one of Columbus best restaurants. They have a fantastic wine cellar with lots of great values. If you are going to dress up some night, hit their bistro (about $30/person) or even just go to the bistro for the wine and dessert. The crowd skews old, so not somewhere to just get out and have fun, but the place is beautiful and its probably Columbus best place for wine. Dinner will run you about $100/each all in.
http://www.therefectoryrestaurant.com/
High Street (part of the area called the Short North and the terms are often used interchangeably) is the trendy area of Columbus. For practical purposes, the part of High Street you care about runs from campus to North Market. Bunches of restaurants with all kinds of food styles and flavors on or near high street. Hit Yelp to see the restaurants there and if there's any that look interesting. The yelp reviews are not to be trusted, but you can at least get a feel for what food options are there.