Consider a family that's living in Hogsmeade. Do they have to bring their children to London (Kings Cross) when they're going to be sent to Hogwarts or can they just bring them into the school directly?
It's all entirely speculation but I'd have to guess they'd just take them to the train platform in Hogsmeade near the time in which the Hogwarts Express arrives, that way everything goes as normal from then on. Luggage taken care of and they arrive by Threstal carriage or boat depending on their year.
This is all contradicted by Pottermore, however, which states:
Many pure-blood families were outraged at the idea of their children using Muggle transport, which they claimed was unsafe, insanitary and demeaning; however, as the Ministry decreed that students either rode the train or did not attend school, the objections were swiftly silenced.
Pottermore - The Hogwarts Express
We do not know how relaxed this law can be, though, as we know both Harry and Ron attended school by Car in their second year and did attend school.
Also Headmaster Dippet mentions the possibility to Tom staying over the summer (in the diary flashback scene in CoS)
"The thing is, Tom,” [Dippet] sighed, “Special arrangements might have been made for you, but in the current circumstances…”
So clearly special arrangements can be made for those staying in the school, I would definitely say that permanent special arrangements can be made for those living much closer to the school.
(Thanks to @BMWurm for finding the quote special arrangement)
They don't have to travel via Hogwarts Express, they could probably walk to the station from Hogsmeade. In OotP Harry returns to Hogwarts via the Knight Bus, which drops him off outside Hogwarts, so they don't have to travel to King's Cross.
They were to return to Hogwarts on the Knight Bus the following day
And they arrive at Hogwarts gates.
They were rolling through a snowy Hogsmeade. Harry caught a glimpse of the Hog’s Head down its side street, the severed boar’s head sign creaking in the wintry wind. Flecks of snow hit the large window at the front of the bus. At last they rolled to a halt outside the gates to Hogwarts.
I imagine the reason that other students seem to use the Hogwarts Express is that it's a bit of a rite of passage, nobody knows where Hogwarts is (so outside of Hogsmeade you can't walk there), and the Knight Bus is an unpleasant mode of transport.
“I’ve changed my mind,” muttered Ron, picking himself up from the floor for the sixth time, “I never want to ride on here again.”
Harry and Ron also travelled via a flying Ford Anglia in Chamber of Secrets, but this was seen as unorthodox.