What I love about The Hobbit and Lord of the Rings by extension is that it utilises the old and known "home is found in people we meet" while simultaneously carrying a message that home is also a place. It can absolutely be a place, one in which memories are kept and one, just as the hobbit hole, means comfort.
Bilbo Baggins will absolutely meet new friends and company he is comfortable with, one that opens his urge for adventures and shows the world beyond what he knows, an experience he will cherish and write down. But Bilbo also wants to return to Bag End.
Not because the Company he grows close with isn't enough of a "home" for him, and not because the adventure he goes on is in any way unfulfilling, but because Bag End, his house, in his home in the most literal meaning of this world.
It shows there's nothing shameful in missing a physical place even when you're being filled with new equally exiting and saddening experience. Because home is a place.
One can move a thousand times and find tens of great companies that will bring new home to you, but there's nothing that will replace the creaking floorboards of your childhood home, or the squeaky matress of your first ever bed, or the exact way the little magnets are positiont on your family fridge. It is connected to memories, yes, but it also connected to your routines, your own way of life.
Bilbo misses his warm tea, and his armchair from which he could see his leaving room, and his breakfasts and the flower in his garden. It is the life he likes and feels equally comfortable with, and it something that is utterly natural to him, and is never shown as bad.
Even when the narrative progresses and Bilbo finds joys in adventures and lands beyond, his yearning for Bag End isn't changed because the story doesn't see it as something that should be "fixed". An adventure is an added new experiment to his life, the one he learns to love, but it's not a replacement for his house, or his tea, or his armchair.
Both Bilbo and Frodo miss home, both Bilbo and Frodo find people they can almost call their another "home" and yet they also miss the Shire, they miss the memories, they miss the place.
Because a home can be a place. Because there's nothing unusual in an experience of opening a door to your own house and thinking "I am home" and there's nothing unusual at missing it in particular when you're away.