Sadly, you are moving to a bit of a twilight zone as far as coarse angling is concerned. The only saving grace is that it's not Northumberland or further north into the North Yorkshire Moors National Park.
I can think of one club for definite and another that's a maybe. The definite is, as mentioned by Wrighty, the
Scarborough Mere Angling Club. The other was reputed to have a pond to the north/west of Scarborough. However, in all the time I spent over that way (over ten years), I never bothered to get to the bottom of it. I suspect that your first port of call should be the tackle shop in town.
There are a few day ticket stillwaters in the area. The obvious one, as Wrighty mentioned, is
Rosedale in Hunmanby.
Two others a little further away, but still in easy reach, would be
Wykeham and
Brooklands.
There's also a small fishery at
Thorpe Hall in Rudston.
If you are happy to travel a bit further west down the A64 to Malton, a few more options open up to you. South of Driffield there are plenty of stillwaters, from farm ponds to gravel pits.
