Final answer:
Austin’s most prominent type of tourism is cultural tourism, with a focus on music and creativity, as suggested by its slogans 'Keep Austin Weird' and 'Live Music Capital of the World.'
Step-by-step explanation:
The type of tourism most prominent in Austin, Texas, is cultural tourism, particularly centered around its unique ethos of music and creativity. This is evidenced by the city's popular slogans such as 'Keep Austin Weird' and 'Live Music Capital of the World', which celebrate its distinctive cultural identity. Despite Texas being known for its socially conservative roots, Austin stands out with its eclectic embrace of different cultures and ideas, as suggested by local billboards declaring it the 'City of Ideas'. Moreover, Austin's tourism draw is not based on exceptional natural resources but on its vibrant cultural and music scene, which includes various festivals and live performances that attract visitors.