I would say La Piola, the little brother of Piazza Doumo, on the ground floor right on Pzza Risorgimento in the middle of town, friendly and bambino should fit right in. But make a booking in advance for Saturdays.
Thank you villasampaguita. But after much reading, it looks like Asti will be more economical travelwise with a baby. I found out from slowtalk that you are a B&B in Asti! Any recommendations for Asti? Many thanks!