You may also be looking for the similarly named facility on Melina II.

The Taylor Hospital was a medical facility on Nel III, located in the Gray Municipality.

In 2368, Peter Lauritson from the Alpha Municipality was treated here for a coma of unknown cause. It was later discovered, that Lauritson had in fact been subject to a telepathic memory invasion by the Ullian Jev. (TNG: "Violations")