Sightseeing functions as a verb (present participle) meaning “to visit places of interest as a tourist.”
“We spent the afternoon sightseeing in Kyoto, hopping between Kinkaku-ji, Fushimi Inari, and the Gion district.”
“Sightseeing” is a compound verb (sight + see). The past tense is often periphrastic: “went sightseeing” or “did some sightseeing” rather than “sightseeed,” which sounds awkward. As a gerund, it’s very common: “Sightseeing is exhausting in the heat.”