My daughter lived in Vicenza for 3 years while her hubby was stationed there. We visited the area twice and Venice 4-5 times while we were there. I agree, enjoy the city because there is none like it.
As for wine, we always made a point to get to Vo, near Vicenza. There are many wineries from mom and pop shops where you knock on their back door for tastings and purchase on up to large, beautiful wineries with tasting rooms similar to Napa/Sonoma. There are so many options you really can't go wrong in any direction. Vineyards as far as the eye can see. I would go back in a heartbeat!
EDIT: OOPS! Just noticed you only have 1 day. Bummer! What JohnT said!