You may also be looking for the similarly named facility on Nel III.

The Taylor Hospital was a medical facility on Melina II, located in the Gray Municipality.

In 2368, one of Taylor's doctors, Rich Thorne diagnosed patient Gary Hutzel with the Iresine Syndrome. It was later discovered, that Hutzel had in fact been subject to a telepathic memory invasion by the Ullian Jev. (TNG: "Violations")