Quote Originally Posted by OracleofWuffing View Post
Besides the 4 Island Guardians, you can also stop by the motel on Route 8 and start the quest to capture Ultra Beasts- you get special pokeballs that you may choose to use for those, but any pokeball works on them. Completing that quest adds one more pokemon that hangs around but is not considered an Ultra Beast by the Commision of Considering Things To Be Ultra Beasts. Ultra Beasts and Kapus can be used in the Battle Tree, the not-Ultra-Beast cannot.

There are no roaming pokemon, so those are the "best" uses for a Master Ball. Aside from any random shiny that might show up.
Also, there's a missable battle with Sina and Dexio on the way to the Battle Tree — it shows up if you walk from the fly point at the port, but the trigger location can be missed if you go in from the fly point to the east.