My wife and I have just enjoyed a delightfully relaxing weekend in Staithes. The owner, david, provided plenty of local information when we arrived and provides excellent accommodation in a well appointed B&B where nothing is too much trouble. Outstanding selection available for breakfast, I can heartily recommend the kippers! We ate out at The George, almost directly opposite The Endeavour, they have a good selection of standard pub fare with portion sizes well above average, at a very reasonable price. They know how to sear a steak properly, try one!
We walked from Staithes to Runswick Bay (and back) along the Cleveland Way, easy enough route although a little muddy, but It is January... Thoroughly enjoyable route but there are others if you fancy something shorter.
There's little to no mobile signal in the area, although there is Wi-Fi in the rooms it's weaker the higher you are, but this can be a good thing!