I was in Ocracoke two weeks ago, wish I was going back soon.
From Winston, I would drive to Cedar Island and take the ferry. Time is the same, but it's less driving for you. You can make reservations on-line to be sure you get a spot; it's $15.
The wife and I stayed at Blackbeard's Lodge. It's one of the oldest buildings on the island, they have a game room with pool table, swimming pool, and they are close to everything. Reasonable prices too.
There is a large beach access just outside the village on Hwy 12 that you can drive to in under 5 minutes. Like mentioned, no beach front property but that is a positive. Lot's of watersports activities, boat tours, etc.
If you want to get off the island to do something, plan around ferry schedules. The Hatteras ferry is 12 miles away and runs all day. You can easily make a trip up to Hatteras if the kids are interested in climbing the light house. The ferry was running slow because after the hurricane the channel has filled in. The ferry literally came to a complete stop and then pushed over the sand to get through.