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Location. Greyhound Hotel is located in Penrith's Lake District neighborhood and attractions in the region include Lowther Castle and Gardens, Appleby Castle, and Dalemain. Regional points of interest also include Rheged and Penrith Castle. Property Features. Greyhound Hotel features a restaurant and a bar/lounge. The inn serves a complimentary full breakfast in the breakfast room. Additional property amenities include tour assistance. Guestrooms. All guestrooms at Greyhound Hotel feature coffee/tea makers.