Not sure about 'lots' to do, sorry, but Whitby itself is very quaint, lots of interesting little shops, outdoor shops, lots of 'goth' shops, great fish 'n' chips. We love Whitby 
Captan Cooks haven is beside an old rail walkway, fab walks either way.
Whitby has links with Dracula, Bram Stoker was inspired by the abbey ruins (I think).
Also lots of boat trips/sea fishing, think can get coarse fishing on rivers in the area.
Scarborough nearby, good 'cheap' shops, very bucket & spade ish,
FlamingoLand zoo/theme park not far.
Robin Hoods Bay nearby great quaint little place about 1 mile from Whitby, lots of 'fossil' shops, great 'fossil hunting'. Very picturesque too if anyone into photography/painting.
Hope this helps, realise might be a bit far for you.
Hoseasons are quite good though, their website is well laid out, you can pick area then narrow down easily into places with indoor pools, allow pets, hot tubs even etc
Yorkshire Cottages are good too, have links with cottages in other areas too.