Hunmanby station is on the branch line Scarborough to Hull which passes through Seamer, Filey, Bridlington, Driffield and Beverley with trains every hour or so from 7a.m. til 8p.m. (fewer on Sundays and in low season). Connections to main line at Seamer and Hull.
If you are a railway fan, North Yorkshire Moors steam railway is only a short drive away or why not make a booking to coincide with the passing of the occasional steam train?