There's a saying I heard a long time ago...in the US 100 miles is nothing and in the UK 100 years is nothing.

Salisbury Cathedral is actually the "new" cathedral. You're right it was built in the 1200's. I've been as far up the spire as you can go, many years ago before they renovated it. From there you can see the hill outside of town where the original church and settlement (called Old Sarum) used to stand. It's just an unearthed foundation now, but still impressive. I recommend seeing both to get an overwhelming sense of your own mortality

Hever Castle is good too. Hampton Court also has a hedge maze though and is an easy trip to Richmond just west of London proper.