I moved back to the US last summer, but really tried to make it a priority to see something new at least every other weekend. I wish I had more efforts to get further from the south, but spending all day on a train and then all night made it difficult, and I often couldn't get friends to go too far with me for trips. Lucikly, quite a few people were happy to do things and around London, especially with the 2 for 1 deals put on by the train companies. I've seen the free museums lots of times, and when I return (hopefully next summer!) I can work harder to see more!
I was always very sad that I couldn't get to Chatsworth House because the nearest train station is a bit far, and its an 8 mile walk from there to the house! I found not being able to drive difficult, and I think I couldn't handle learning to drive on the opposite side and using a manual gear.
Leeds Castle and grounds was really lovely and Kew Palace/Gardens was one of my favourite days out (even though I was poo'd on by a bird!)