I was just in England last month, and my husband and I took a day to visit Oxford. The email address to contact the head resident at the Kilns is
thekilns@cslewis.org. Her name is Teresa (at least, I believe Teresa will still be there through the summer), and she's wonderful. Very warm and kind and helpful. The tour of the house takes around an hour or so (and keep in mind, they ask for a 10 pound donation). And you can ask Teresa for directions to Lewis's church where is also buried - it's only a mile or so away.
From there we took the bus into town, walked up to the Eagle and Child for lunch, and then walked down High Street and toured Magdalen College. It costs a few pounds and they give you a little brochure to take you around the grounds. We walked along Addison's Walk and if we had had time, might have even rented a boat to take down the Cherwell (which is the canal that runs along Addison's Walk).
We had also wanted to take a tour of the Bodleian Library, but we didn't have the time (it closes around 5 or 6pm).