Not been to that one but if you want closest have you tried Rountree Caravan Park in the centre on the riverside (as long as it is not flooding) and one I have been to with a caravan a few years ago is the Rawcliffe Manor Caravan Park just off the A19 going in from the north just past the A1237 ring road... this one has a dozen pitches at the rear of a pub and close to public transport from a Park and Ride site.
There’s Naburn Lock a couple of miles outside York with a river bus service into town. The site does tend to flood though, I saw it under about 4 feet of water a few years ago.
Nora
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unfortunately going to York needs to be planned months in advance, chances of getting into most of the sites will be fully booked, you would be best looking further outside of York and driving in expect to be around 15 miles away minimum, Rowntree park site needs booking at least a year ahead!
Naburn lock site is very good with bus stop outside site or river bus. We haven’t had much rain up here recently and all rivers are at very low levels at the moment.
Borough bridge c&cc site is about half an hour drive to poppleton park and ride. Don’t attempt to go into York with car. You can do railway museum minster and Jorvik in a day. Then you’re free to visit the rest of the Yorkshire dales, Knaresborough (6 miles) Harrogate (10 miles) Ripon (6 miles) enjoy your trip.
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We were at Pear Tree Farm in Harton recently and it's about as lovely as caravan sites get. It's about 9 miles from York, 30 miles from Scarborough and 15 minutes drive to Castle Howard.