I went on a Tudor tour of my own in 2003. As a huge Anne Boleyn fan, I strongly recommend Hever Castle. Hampton Court is wonderful and is easily accessible via train, but I'd recommend the many tour boats that run from London via the Thames. Sudeley Castle was great as well, but definitely further away. Windsor is fascinating but less "Tudor", although St. George's Chapel is amazing and Henry VIII and many others are buried there.
The one place not mentioned so far that I enjoyed was Hatfield House, just north of London in Hertfordshire. The tree where Elizabeth I received the news of becoming queen is still there, as is the Old Palace where she stayed those many years as a youth. You can only see the inside of this building during an evening dinner that you can attend, which is supposedly in the Tudor tradition as well. The Jacobean main house is beautiful too, built by the Cecil family. From their website.... The main entrance to Hatfield Park is opposite Hatfield station with a 5 minute walk to the house. The fast train from Kings Cross to Hatfield takes 25 minutes. There are London Underground links with this mainline at Finsbury Park (Piccadilly and Victoria lines).
I'm soooo jealous. Enjoy your trip and report back to this armchair traveler!
By the way, as a 40 year old woman, I travelled alone to most of these places. It was just fine. I felt very comfortable using all types of transportation mentioned here and people were very helpful when I asked for help, mostly on the tube. Just be smart and I'm sure you will have a safe trip!