Laura, have a look here at this Backpackers accomodation. I know a few folk who stay there but you might need to book up early.Its down by the river so no hills to climb.
http://www.whitbybackpackers.co.uk/contact.htm
Kenn and Birgitta Ward-Foxton
YO22 4EF
England
Tel: (0044) 01947 600817
Mobile: (0044) 07779 798611
.