Ammonite Cottage is just outside Whitby, about a twenty minute walk from the centre. It's one of a group of holiday homes, set back from the main road. You get your own decked area out the back.
It sleeps six. Three bedrooms and one bathroom. There's also a separate toilet downstairs. It's a 4 Star place, so it's comfortable and has everything you need. The bunk room has full size beds, so it's fine for adults too. Pets are allowed, up to two.
The main bedroom has a small balcony that looks out at the old viaduct. The Cinder Track, which is the old railway line, runs right past it. You can walk or cycle into Whitby on it, or go the other way towards Hawsker and Robin Hood's Bay.
In Whitby, you've got the beach, the abbey, and the harbour. The 199 Steps up to the abbey are exactly that: 199 steps. It's a proper climb. The beach at Sandsend, just north, is good for families.
If you want to explore, the North York Moors are right there. The North York Moors National Park site has walking routes. The steam railway from Whitby to Pickering is a nice trip, especially with kids. Goathland station is the one used in Heartbeat.
For facilities, it's got the basics covered: parking, wifi, a washing machine, dishwasher. Bedding and towels are included. There's a highchair and a cot if you need them.
Useful links for planning: English Heritage for Whitby Abbey and North York Moors Railway.