If you're in the vicinity of Durham City then it is well worth the trip to see this castle and the cathedral and walk the river walking paths surrounding the city. Visiting during university term time and holiday time can give one a different feel to the place. I was a student there many years ago and the castle was our hall of residence - an impressive monument to have as one's living place. I still go back from time to time, and it never ceases to amaze me that this castle is very much in use daily. Don't compare it to Windsor Castle because that castle is for Royals and tourists (an odd mix!), whereas Durham Castle has young people in the building and it's very much alive.
The cathedral is regarded as one of the finest Norman structure still standing today, so when one combines this with the castle, the ground and surroundings where these buildings stand, plus the shop and teashop inside the cathedral croft - I think one's visit will be most memorable.
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