When we visit Scarborough which is often, we normally stay at the Arosa Camp Site in Seamer so the Park and Ride in Seamer Road is convenient for us. There's a nice garden centre just before the Park and Ride so we call in there, have a look round and a bite to eat in the cafe then move on to the Park and Ride. Buses run every 10 minutes or so. And last time we had my elderly parents with us, they love camping too and they were able to use their bus passes for free rides into Scarborough.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.