Consider joining a "community supported agriculture" program. This partners you with a local farmer to buy a share of their meat, vegetables, or eggs for the season and you can pick up the food at a location in Columbus.
http://www.localharvest.org/


http://www.eatwellguide.org/search/summary . This site also features guides to local bakers, stores, restaurants and "buy local" organizations

Farmers

Frijolito Farm 2130 Paul Drive Columbus, OH 43211 614-390-2692 (5.13 miles)

Just This Farm 7657 Feder Rd Galloway, OH 43119 614-805-5776 (7.68 miles)

Bramble Brush Farm 10819 Johnstown Rd. New Albany, OH 43054 614-855-6874 (14.62 miles)

Farmers Markets

Upper Arlington Farmers Market 2100 2100 Arlington Ave. at the Mallway Upper Arlington, OH 43221 614-674-4719 (0.00 miles)

Bobo's Trade Day 74000 OH-124 Langsville, OH 43210 740-669-4455 (2.55 miles)

Clintonville Farmers Market 3509 N. High St. to 3559 N. High St. Clintonville, OH 43214 (614) 262-2790 (3.54 miles)