We would like to rent a car in Genoa and travel around the Barolo wine region on a day trip. Is this doable and are there any recommendations for wineries in the area.
Yes, it should be doable. I would drive directly to Asti and then on to Alba.
Check out this website: http://www.decanter.com/wine-travel/italy/wine-trails-eight-piedmont-wineries-to-visit-285066/