Mayweather and Tucker in the "sweet spot" aboard the NX-01
The "sweet spot" was a location aboard most starships in the 22nd century, where the artificial gravity field became inverted, leading to a reversal of the vertical orientation relative to the rest of the ship. Usually located approximately halfway between the bow plate and the artificial gravity generator, Travis Mayweather would spend a large amount of time in this location while growing up aboard the ECS Horizon.
In 2151, Mayweather showed this location aboard the Enterprise NX-01 to Commander Charles Tucker. Two years later, Mayweather retreated to the same spot upon learning of the death of his father. (ENT: "Broken Bow", "Horizon")