I have a soft spot for those three
ATOMIC SUPLEX , all are easy(ish) to get to by train.
All have plenty to do, a bit too much in some cases.
Whitby can get crowded and pricey, but there are self-catering places as well.
Scarborough has a "kiss-me-quick" reputation and I think has generally gone a bit mass/down-market.
York is very diverse and well connected ...
Berwick, North Berwick, Seahouses, Whitley Bay / Cullercoats ... all alternatives but, unfortunately, Seahouses is not on the rail network, so maybe scrub that one.