Where to go for a week's holiday in Yorkshire?

[MumNeedsTea]

As the title suggests, I'm looking to book a week's holiday in Yorkshire, but I have no idea where to stay. This will be over the October half term break and we are a family of 4 with 2 DSs (almost 5 and 9 years old).
I would like to stay close to the national parks, with the option of having a day trip to the coast if the weather looks good. I do realise that given this will be in October, we may not get any good beach days.

I cannot decide whether to stay close to the North York Moors or the Yorkshire Dales. We will be driving from Kent if that matters. We're looking for self catering cottages/apartments.

Also, if you have tips on things to do and places to visit, that would be very helpful. We have never been to Yorkshire and as such have no idea where to start. I just want a break from our usual New Forest/Cornwall/Devon holidays

Thanks!!

I have fond memories of an October half term in York when I was younger - a lot to do in the town plus a chance to get out to Castle Howard, Whitby etc

Thank you all for your suggestions!! I've finally booked an apartment in York... About 15 mins from the city centre. It's for 6 nights, so the plan is to spend 2 days in York and the rest between the national park and coast (if the weather allows).
I can't wait for October

The day after we get there is DH's birthday.. Any recommendations on something special we can do for him in York?

*for something special

Saltburn!