I did it in my 34 a year ago.
Took the Albemarle/Chesapeake ICW route (I've heard there's been some depth problems in the Dismal Swamp Canal). We did Norfolk to Oriental in 2.5 summertime days (Sat AM to Monday noon). Could have arrived Sunday night but stopped sailing at sunset each day (a smart idea since there's a lot of nighttime barge traffic - they figure we're out of the way by then).
The trick is to time the locks. There's lots of info on the web. We had a book of maps that had pretty useful notes.
The other trick is to have a very reliable engine. You're going to motor the majority of the miles from Norfolk to the Neuse in fairly narrow canals. You don't want to get stuck in these places (I'm looking at you, Allegator-Pungo).
Fenders and ropes are also important.
My speed aside, I recommend taking it slow. It's a beautiful trip - lots of very quiet, wild places to anchor. Lots of neat watering holes as well. But if you're in a hurry, it can be done pretty quickly in the right conditions.
As for inside, outside, ICW: The ICW is a safe, proven route. I wouldn't go outside this time of year (there's been a news story about a lost sailboat outside Morehead City every week for the past month or so, and lots of Coast Guard activity). Inside (Currituck/Croatan) there are still some low bridges and other issues.