The Landings is located directly on the seafront.  Its address is:

7-8 The Beach
North Yorkshire
YO14 9LA

You can park directly outside to load and unload. You can also park directly outside between 18:00 and 10:00 (please check the signs to see if this is still current). The parking bays on the opposite side of the road can be used for the duration of your stay. You probably won’t be able to find a free one during the day, but from around 18:00 they become free. There is also free parking up Crescent Hill and around Crescent Gardens.

There is long stay parking at the end of West Avenue and the current charge is £7 for 24h, though if you don’t intend to use your car you can move it down to The Beach in the evening.