Algernon is planning to go to the country to visit his friend Bunbury. This can be inferred from the dialogue between Algernon and Jack, as Algernon mentions that he is going to "kill [his] poor friend Bunbury," a reference to visiting his friend under false pretenses. Additionally, Algernon mentions that he has arranged for his dog-cart to be sent to him, indicating that he is preparing for his trip to the country.