Basically there are two major tourist attractions in Dover. One of them is the Dover Castle, called the "Key to England", the largest castle in England and obviously the White Cliffs of Dover.
Personally I wanted to have a proper walk rather than wander most of the day around the Dover Castle, so I skipped it. I liked Dover so much, that I actually had to skip it, to have a reason to get back there!
Oh, oh, and obviously the third greatest tourist attraction are sheep... unfortunately this cute fellow behind bars.
Next city east from Dover is St Margaret-at-Cliffe.
It has very nice bay called obviously St Margaret's Bay. Wikipedia says the the cliff above the bay is the one where the sun is supposed first to reach the UK every morning.
I should have spent more time there, it's a pity I did not... oh well, next time. Anyway, these areas are awesome. Actually the path I took is a Saxon Shore Way path, from Roman times. The plan is to get back there with a bigger backup of time and go even further. And at the end!