I had a Travelodge discount code ('AUTUMNSTAYS') which was supposed to expire last week, but tried it and it worked. Had intended to look at the price for the one at Parrs Wood, but the one nr Heaton La. was cheaper - with code, £38 for 'family room' (as they don't offer twins).
Re the route, I never usually advocate this, but consideration might be given for a taxi from one of the lower locations to the higher, eg Railway... to Olde Vic (depending on running order)