We’ve holidayed at the Bay the last few summers and will do again this year. There’s cycle hire and maps just off the main road at Hawsker before Robin Hoods Bay which is probably your best bet to start: Trailways
It’s got info on the Whitby to Scarborough coastal rail trail (on old railway funnily enough) so I’d imagine it’s not too rough. Not done it though so can’t say for certain. Our youngest was 1 when we first took first there, will be 4 in summer this year and she loves it and can’t wait to go back.
Lots of nice walks to do – along the cliff path to cafe at Boggle Hole youth hostel, then back along the beach is a fave of ours.
Falling Foss Tea Garden does great cream teas and is a nice wander through the trees for all ages.
Crab fishing in Whitby harbour.
Messing about on the beach at Robin Hoods Bay, Whitby, Scarborough.
Peasholm park in Scarborough for general park fun, swans, dragon boat rides.
Playdale Farm Park not far from Scarborough.
Further afield is Flamingo Land though we reckon it’s too costly.
Not that far from Dalby Forest.
North Yorkshire Moors Steam Railway is nice (though wasn’t impressed with Goathland where they film Heartbeat, Grosmont was much nicer).
Suppose it also depends what kind of holiday you want. We liked to explore and relax and found it perfect.
Oh and there’s a great chippy in Robin Hoods Bay, and ice cream, and highly recommend Hadley’s chippy in Whitby.
When are you going?