All Out of Universe:
Why did it also take Arnold so long to find John? - I highly doubt that the Leader of the Resistance forgot to include his childhood address when he reprogrammed 'it' to be his protector.
Again, as I mentioned in a comment, this is so that we can introduce the "bad guys" at night and the "good guys" in the daytime, leading up to the spot for the final transition into night, 2/3rds of the way into the movie, just like every other movie ever.
This also mirrors the introductions in the first movie: "Guard it for me, Big Buns." Except this time, the music was better.
Offscreen Inertia –TV-Tropes
As long as a character is offscreen, it's assumed that they continue doing whatever it was we last saw them doing.
Obviously, the computer in the car must have had a TV-trope link; how else do you lose 8 hours of your life?
According to Google, the commute from where the T-1000 appeared to Reseda is about an hour. At 4am, traffic would be negligible and had it gone directly to John's house, the movie would have been over rather quickly.
I'm sure there's another trope that addresses playing merry havoc with day and night. You're free to spend you entire life looking for it ;)
Ultimately : Why? - Because cinematographic plot device character development, that's why. See also, The Script.