I need more context to figure out the exact meaning. From the text, 登高 climb up high, 远望 look faraway, 别 secially, 有 there be, 一番滋味 some feeling or emotion, so 别有一番滋味 there is a special feeling in my mind. Maybe just be amazed by the gorgeous scenery, maybe miss family and friend faraway, maybe nostalgia... Hope this help .☺