I’ve been to Warwick Castle. Fantastic place. Make sure you take enough time to visit the gardens. When I stopped at York, we had time for only one site visit. We chose the cathedral. Glad we did, but it would have been nice to see Jorvik as well.
If military-type museums are to your taste, I recommend RAF Duxford South of Cambridge. The market square in Cambridge is worthy of a visit, in it’s own right. The Naval museums in Portsmouth are a must, if you have time to see HMS Victory. Then there is Dover Castle......Chatham historic shipyards...
Edinburgh Castle and Holyrood Palace.....I won’t even mention a certain big city.
Of course, I was over there for 1.5 years in 1991 - 1992, working on a DOD contract, so I had much more time than you likely will.
Thank you for the suggestions. We’ll probably have a week, so we’ll have to plan judiciously.