Both stories start from a point where everything seem to be banal and ordinary. But still, there's a smell of adventure right after that corner...
The house:
"It was the sort of house that you never seem to come to the end of, and it was full of unexpected places. The first few doors they tried led only into spare bedrooms, as everyone had expected that they would; but soon they came to a very long room full of pictures and there they found a suit of armour; and after that was a room all hung with green, with a harp in one corner; and then came three steps down and five steps up, and then a kind of little upstairs hall and a door that led out on to a balcony, and then a whole series of rooms that led into each other and were lined with books - most of them very old books and some bigger than a Bible in a church. (chapter 1-Narnia)
In a hole in the ground there lived a hobbit. Not a nasty, dirty, wet hole, filled with the ends of worms and an oozy smell, nor yet a dry, bare, sandy hole with thing in it to sit down on or to eat: it was a hobbit-hole, and that means comfort. (chapter 1-Hobbit)
The characters:
[Peter] "I'm going to explore in the house."
Everyone agreed to this and that was how the adventures began." (chapter 1-Narnia)
"This is a story of how a Baggins had an adventure, and found himself doing and saying things altogether unexpected." (chapter 1-Hobbit)
The fantasy happens. Both stories have a sort of portal where the fantasy and adventure enters in their lives. In The Hobbit, Gandalf enters Bilbo's door and surprises him with this unexpected journey they must take. In Ch. of Narnia, the children are the ones who enter the fantasy world by mistake. But as they say, there are no accidents!
Coming home?!
This fantasy world is very harsh with those who are not familiar with and they have to adapt. Most of the times, especially in The Hobbit, Bilbo wishes he would have stayed home in stead of wandering randomly. Fantasy is not for everybody, but it's still good afterall.
"Bother burgling and everything to do with it! I wish I was at home in my nice hole by the fire, with the kettle just beginning to sing!" It was not the last time that he wished that! (chapter 2) and the wishes continue
In Narnia, Lucy remembers that she has to come home. She had enough fantasy already: "Oh, Mr Tumnus - I'm so sorry to stop you, and I do love that tune - but really, I must go home." (ch.1)
It's very hard to find your way home when you are clearly in another world where the word "home" doesn't exist for you. But after a few strolls you find out "other" homes that you might like: the beavers' home, Aslan's home, the Witch's home etc. But in The Hobbit, the only one who thinks about his home so deeply is Bilbo. Because for the rest of them, the new home was their treasure and Bilbo had nothing to do with it personally. That's why it was very hard for him to adapt to their new situation: starving and still fighting to survive.
Is there a pure fantasy that doesn't rely on what people already know?