Good topic & good choices.
When I lived in Winchester I used to love to walk through the cathedral grounds and then out of town along the Itchen Navigation to St Cross:
http://hospitalofstcross.co.uk/
It's a former hospital and almshouses rather than a church but I hope I can bend the rules as it's such a peaceful, beautiful spot. It's a shame that by the time you climb nearby St catherine's Hill sound of the Newbury bypass becomes hard to ignore.
Also, coming from Chesterfield it would be remiss of me not to mention the beloved Crooked Spire (aka St Mary's). The sight if it from the train window is a sure sign I'm back "home" even though I live in Sheffield these days.