A drive, with some walking around various bits of the pretty seaside villages and towns along the way.
Staithes is unbelievably pretty and photogenic. Don't be put off by the uninspiring village at the top of the bank. The village at the bottom is worth the walk.
Runswick bay always seems to be warmer than the rest of the coast, due to the south facing, sheltered location overlooking the bay. The walk along the beach is brilliant, and in summer it's a pretty decent swimming beach to. In nice weather, the pretty red tiled houses, and the lush greenery with the wide bay behind look like something from a far warmer climate.
Whitby needs no introduction. Some parts are like a coastal town anywhere, with tacky seaside features like you see anywhere on the English coast. The area below the abbey, although touristy, is a treat. Keep a look out for goths. Although crowded with goths during the 'season' you'll be sure to see a few at any time of the year. During summer, the goths do look a little bit out of place amid the people dressed in beach clothes. Fish and chips in Whitby is a must do. The Magpie is famous, and has queues outside to match, but there are other great places to eat in the same area. If you need to burn off some food, walking up to the abbey, especially at sunset is a great place for views, especially of the sunset.