So I live in the western United States and I am going on a trip to Paris/Versailles and London. I am seeing the Versailles palace and will try to make it to the Compiègne Wagon Museum.
Is there other historical sites I should put on the iternerary?
When you visit the palace, make sure you walk through the gardens! I was there a couple of years ago and on a weekday afternoon the gardens were pretty deserted. We were able to take our time and have a leisurely stroll and really enjoy the beauty and solitude that they have to offer. We didn't actually go into the palace while we were there (packed crowds that aren't concerts are a big 'nope' for both me and the person I was with) so I'm not sure if it has less busy times when you can take your time and in the atmosphere, but the gardens definitely do and it's a pretty magical experience.
Also, directly across the street from the palace you will find the Royal Stables. The Great Stables is home to the Equestrian Academy of Versailles and while they have paid dressage shows you can see, you can also just walk through the gate onto the grounds and catch the riders working with horses in a small training arena in the courtyard for free. I don't know if horses are your thing, but as someone who grew up around them and dreaming of riding in the Olympics, it was one of the coolest things I've gotten to see anywhere. The horses are beautiful and well trained and the riders are skilled so even if you're not a horse person, it might be something you'd enjoy spending a few minutes watching.
You should also take the time to walk around the area near the palace, especially around sunset if you have a chance. The way the light plays off the buildings and statues is gorgeous and there's history everywhere you look. There's also a little pastry shop not too far from the palace grounds called Aux Pains de la Ferme that has fantastic fresh pastries and coffee and the staff are very forgiving if your French is less than perfect.
If you have the time in your schedule to make a side trip to Reims, I would strongly encourage you to do so. It's roughly two hours each way either by car or public transit and the Reims Cathedral is just honestly breathtaking. It's impressive on a scale that my poor little American brain has a hard time comprehending even now. haha I was very literally awestruck when I saw it and even more so as I walked through it. It's almost like in that cathedral (and every other cathedral and church I've been into in Europe and the UK) you can feel the history in the air around you.
As for London, I would say to see what kind of exhibitions the British Library has when you're going to be there. When I was there in 2016, they had an exhibition on the history of punk that we really enjoyed. As someone well versed in American punk history, I enjoyed the hell out of seeing 'the other side' of it, so to speak. They have multiple exhibitions at any given time, so there's always a chance there will be something of interest to you.
If you're in London on a weekend, make sure you visit the Camden Market! I think it's open every day, but some of the smaller shops and such are more likely to be open on the weekends and imo you get the full experience that way. It's really crowded but doesn't feel claustrophobic a lot of crowded places do and there's just so much going on. There's so much to see and hear and smell whether it's street artists or random music or the shops or street food stalls or just watching people be people. My favorite part was the Stables Market because it's kind of a maze of back alleys where you can find smaller crowds and some really interesting small shops. Although the entire market is pretty historic, I think that's where you can see and feel it the most.
There's also a little street food market that's kind of enclosed in a courtyard (the food section of this guide tells you where to find it) that has a huge selection of street food from different places around the world. I'd recommend it over any restaurant you're likely to find in the area because in addition to incredible food, it has a great atmosphere. In general, Camden Market is a great place to pick up some unique gifts and souvenirs as well as being just a really fun place to visit.
I loved visiting both Versailles and London and I hope you have a great time on your trip!