For this trip, I did stay at the Wessex Hotel in Winchester, but my favorite hotel in the area is the Potter's Heron, which is just south of the IBM Laboratory at Hursley. I like it because it's close to the Hursley village and the IBM Lab, but also because it's out in the country. I almost always have a rental car, so getting places is not a problem as it might be for some, expecially first time visitors.
Here is a picture of the Potter's. The main entrance and pub is a thatched roof building however the sleeping rooms and restaurant to the rear of the property are all fairly new facilities.