if you don’t already have a base, Ox Pasture Hall hotel on the way towards Scalby is quite nice – provided you don’t get a room above either (a) reception or (b) kitchen
not sure if they still do it but they used to have scale model naval battles on the lake at Peasholm Park. Marine Drive can be quite ‘bracing’ if the wind is up. The Grand Hotel is a Butlins. Yorkshire County Cricket Club sometimes play at North Marine Road. They used to have motorcycle racing at Oliver’s Mount, don’t know if that still happens
Being from Leeds when I was a kid we used to do day trips to Scarborough, Bridlington, Whitby, Filey but TBH I wouldn’t know what to do with my time in any of these places as an adult