I’ve been living on the edge of the NYMs for the last year, so not an expert but I’ve done quite a bit exploring. For me the road riding is exceptional, really top notch. Quiet roads in good condition, great scenery and challenging climbs. I find it a very “low stress” place for road riding versus any of the other English National Parks due to the good road network and low traffic. It’s great being able to ride up on the moor and stop at the beach in the same ride. If you’re in Filey I would take the road bike.
The mountain biking is very extensive and a great way to explore. It’s not got the extensive gnarr of the Lakes or Peaks but there’s plenty of singletrack and some good downhills. Again, the extensiveness and quiet probably set out from other parks. If you’re some sort of enduro warrior you might be a bit underwhelmed by the miles of moor top pedalling.