Located in Roppongi Hills Mori Tower, the Mori Art Museum hosts regular exhibitions from artists from around the world. While the museum is not as extensive, the ticket price includes access to the observatory where you can enjoy amazing views of Tokyo.
The museum generally has modern art exhibitions in a variety of genres, including fashion, architecture, design, photography, and video.
Find the latest and upcoming exhibits at their website here:
https://www.mori.art.museum/en/exhibitions/index.html