In that case, from the YH in Beverley you can easily do 6 mile walks:
up onto the Westwood and outskirts of Walkington
along Beverley Beck and onto Figham, returning along the other side of the beck
over Swine Moor and along the canal at Tickton for as far as you like before retracing your steps
The Westwood, Figham and Swine Moor are all open access so you can wander where you want although cattle (Westwood and Swine Moor) and horses (Figham) are currently being grazed on there (ancient local bylaws).
Or:
you could catch the bus to Cherry Burton and walk back to Beverley
bus to Market Weighton if you want some hilly stuff
bus to York if you want some quirky urban/historical stuff (go in search of Whip-Ma-Wop-Ma-Gate!)
if you want to lose the will to live catch the bus into Hull..
Around Beverley itself - look up! (as in don't stare at the pavement) all sorts of strange things attached to walls, strung between buildings in alleyways, hanging from flagpoles, attached to benches.
There's a really nice deli/sandwich, fruit and veg shop called Browns in Wednesday Market, by the way.
... anyway, that's enough for now.
oh, by the way, Beverley YHA is haunted ...