Gary Trainor didn’t have to travel far to get to the Grammys on Monday.

“We decided to close our business on Nantucket and go seasonal,’’ Trainor told us by phone on Wednesday, adding that the family’s store, Jewel of the Isle, will reopen in May.

Trainor — Meghan Trainor’s dad — is now spending winters with the family in Los Angeles. Meghan, 22, who was raised on the island and on the Cape, shares a place nearby with her brothers, Ryan and Justin.

Ryan, 23, works for Smashd, which covers tech and culture. Justin, 20, is studying to be a producer.

“To me, it’s amazing that they are still together as a family unit,’’ Gary said.

The elder Trainor, meanwhile, is happy to be on the West Coast for better weather — and to be available for his daughter as her career grows. On Monday, he was her date to the Grammys, where she won best new artist. “She tries to include us as much as possible,’’ he said. Gary said he follows Meghan’s lead at these big awards shows, and has learned that even the most famous recording artists are just regular people. He does admit that it was a thrill to meet Tony Bennett that night.

“What a charming and wonderful man,’’ Gary said.

Gary was seen on national television whispering some words to his daughter just before she took the stage to accept her big honor Monday. Asked what he told her, Gary said: “?‘Oh baby, you made it.’ That’s what I told her before she got the award.’’