Dan. Agree with Pain is... ^ Upper Parliament St, Everton Valley and that's about your lot in the town centre. [I'm from W. Yorkshire too but moved to da 'Pool 14 years ago]
Good ideas above; but if you like some off road, try Crosby beach and the promenade (about 6 miles N. of town); good footpaths past Coastguard Station at Burbo Bank to Hightown.
A bit further up the coast (10 miles N. of town) you'll find Formby Point, a National Trust site with miles of woodland trails, huge sand dunes, coastal vegetation and a magnificent beach, not to mention the red squirrels, which are suffering at the hands of pox carried by their grey relatives

Over the water on the Wirral, seek out Bidston Hill from Wallasey, and the Wirral Country Way. Lengthy promenades and dramatic beaches at New Brighton & Wallasey.