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 was familiar with it from growing up aboard the ECS Horizon.
In 2151, Mayweather showed this location aboard 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")