I’d follow Mike’s suggestion about staying in Haro, but Logroño is nice too. There are plenty of Bodegas in the area. If you were going to be in area area for more than a couple days, you may want to consider a rental car as some bodegas are not right in town. Do not drink and drive. It isn’t worth it.
Logroño has some wineries in town and is known as a great place for tapas. It is larger than Haro and more to do in the evening.
While in the area, there are plenty of places to visit in the small towns in that area, so I recommend not limiting your activities to wineries. When we were there, we had a rental car.
The wine fountain on the Camino is at Bodegas Irache right by the Monasterio de Santa María de Irache. While the wine is free, it is new wine and actually pretty nasty tasting. If you do go there please remember that the wine is there for the pilgrims walking the Camino, not for tourists. Be respectful and sample some, but don’t go filling your 2-liter bottle. There have been occasions where tourists come in busses and do exactly that. FYI, there is a live webcam of the fountain if you want to see it.