Many go to Southampton to catch a cruise, arriving the day before and having the morning of their cruise free until their boarding time. About 15 miles outside Southampton is lovely Beaulieu (pronounced Boo-lou). Though public transportation is possible, it is not easy to access and takes time. If you have two or three going, you can readily hire for a half day a taxi to bring you there and back. The grounds are beautiful (think eastern Tennessee or North Carolina in the fall) and feature a number of attractions--a palace, a church, a motor car museum, and a small but fascinating SOE museum called the Secret Army Experience.
Beaulieu was the last school ("the finishing school") for British SOE agents before they left on their incredibly dangerous missions. It was called the "finishing school." Few, if any, of the many buildings actually used by the SOE remain (someone in the UK can confirm or correct this--but the houses are certainly not available to the general public). The museum is only five or six rooms. Many walk through it in 10 minutes. But if you have some knowledge and interest in the SOE, you can spend an hour there. I spent 90 minutes on a day when there were few visitors and I practically had the museum to myself. The museum has a book that contains the bio of every SOE agent who trained at Beaulieu.