If you’re taking the A169 across the NYMoors then there’s the Bridestones walk (a good one if the weather’s claggy). Sandstone rocky outcrops, not dissimilar to the gritstone rock formations in the Peak District. It’s a reasonable 6 mile walk from Lockton (just off the A169) – free parking.
Alternatively, a bit further up the A169 is Hole of Horcum (best done in decent weather/visibility to get the scale of the hole). I seem to remember doing a 6 or 7 mile walk round there with Andy Broadley of this forum a good few years ago now. There’s parking at Saltersgate but I believe there’s a charge. Alternatively, you could start the walk from Lockton.
Enjoy driving up Saltersgate Bank - hope your clutch isn’t slipping!
As pleb said, Roseberry Topping and Captain Cook’s Monument. Not sure of the mileage but (knowing me) it will be about 6 or 7 miles. Free parking (and fab cafes/pubs) in Great Ayton. It is further inland and up country than Whitby though and probably easiest reached off the A171.
If you’re heading on the northern York circular road and travelling along the A170 then you could head up to Sutton Bank (another nice, steep drive!) and do the Kilburn White Horse walk or Gormire Lake from the visitors centre there (rip off parking charges though). Walks can vary between 3 and 9 miles. Loads of options to choose from really.
Alternatively, a bit further along the A170 (and up a bit) is Farndale and Rudland Rigg though this might be a bit bland at this time of year (best for heather and daffodils seasons). It’s about 6 miles. Honesty box parking at the village hall in Low Mill.
I seem to recall having a route for a walk between Pickering and Thornton-le-Dale (off the A170) via Howl Dale and Kirkdale Slack which would be a semi-urban (in a cute market town and village sort of way) walk if you like to look at forests and thatched cottages and quirky tea rooms. It would probably be about a 5 mile walk.
Right. I think I’ll shut up now!