BOMBA is an elite training school for monster breeders, whose teaching method is focused on monster battling technique than raising method. They have a rivalry with the Elives School, as the institution was founded to give breeders more options. They have their own shrine and battle arena, and as such, one might assume they are located within the city of Borgan.
By the time of My Monster Rancher, the Academy has been established for "a generation" at least. There are many things breeders can do at the Academy, including generating monsters from mystery discs or neighbor profiles, and combining monsters. The Academy also does research on monsters and items, and sponsors some adventures.
Gallery
The Academy Halls in MFDS
BOMBA's battle arena