This is a little theory I wrote about the 24 hour gap:

As we know, in Harry Potter and the Sorcerer’s Stone, Harry Potter and his family (Lily and James Potter) are attacked by Lord Voldemort on October 31, 1981. Harry is then taken from the “almost destroyed” Potter’s house in Godric's Hollow by Hagrid.

The next day, November 1, 1981, Hagrid takes Harry to Number 4 Privet Drive to meet Dumbledore. We also know that somewhere in between these two times, McGonagall meets Hagrid and is told that Hagrid is going to meet Dumbledore at Number 4 Privet Drive on November 1.

We know that McGonagall meets Hagrid because of this little conversation between Dumbledore and McGonagall: Dumbledore- “Hagrid’s late, I suppose it was he who told you I’d be here, by the way?” McGonagall- “Yes, and I don’t suppose your going to tell me why you’re here of all places?”

According to this, there is gap about 24 hours between the time that Harry is taken from Godric's Hollow, to the time that he arrives at Privet Drive. So, where did Hagrid take him?

Here are some options:

The Leaky Cauldron/Diagon Alley- This is a possibility, because there are rooms in which Harry and Hagrid could have stayed, although very unlikely. There would probably be too many people wanting to see “The Boy Who Lived.” And Dumbledore most likely wouldn’t want that, considering he wanted Harry to live with his aunt and uncle because the fame would “be enough to turn any boys head. Famous before he can even walk and talk!” So, that isn’t a very likely place for Hagrid to have take Harry. Plus, how would McGonagall find Hagrid and Harry there?

The Shrieking Shack/Other places in Hogsmeade- This is another possibility. In Harry Potter and the Prisoner of Azkaban, Dumbledore has that he has used The Shrieking Shack and other places in Hogsmeade for hideouts. (He used it for Lupin when he was in school, and for Sirius after he was saved by Harry and Hermione.) So, why wouldn’t he use it as a hideout for Hagrid and Harry? There are two reason why this wouldn’t work. One, how would McGonagall find them in a cave or in the Shrieking Shack? And Secondly, how would Hagrid fly the motorcycle in to Hogsmeade without being noticed? So, that wouldn’t really work.

Hogwarts- The only other place I can think of that Dumbledore would even consider is Hogwarts, and it is probably the best bet. Why? One reason is because Dumbledore knows and trusts everyone who works there. Plus, those who work there trust Dumbledore enough to not tell anyone. Another reason is that Hagrid could get his motorcycle in and out without a ton of people noticing. And, since McGonagall works at Hogwarts, she would most likely be there, and could ask Hagrid where he was going to meet Hagrid. Three good reasons. And, since it is Dumbledore’s school, Dumbledore probably knows ways too get in and out of Hogwarts quickly, and can get to Hagrid and Harry if anything goes wrong.

Although this has not been proven, according to the information above, it is most likely that Dumbledore had Hagrid take Harry to Hogwarts for the 24 hours or so before leaving him on the Dursley’s doorstep.