From New Bern Grande, Beaufort/Morehead is a long trip for lunch. That's more of an overnight thing. Both are great towns with different experiences to offer. The Morehead City Yacht Basin is your target for there. Nice big face dock and wind would be your only beast. Beaufort is a much trickier approach. Along with wind, Taylor's Creek run pretty fast, so always plan on getting there at slack high or low. The dock hands are very good there, but have little patience if you don't listen to them. The facilities (shower and head) are for the 70's and suck pretty bad. Just shower on the boat. Morehead's team and facilities are stellar.
Anyway, your lunch trips will often be to Oriental. It's a great little walking town. Prefect for a day visit. You will call the Oriental Marina on VHF 16 and will probably get the face dock for a lunch run. They also have two free town docks and you can check the webcam for availability, but don't expect much during cruising season or summer weekends.
The other thing is to come throw the anchor out for an overnight of just a day of sunning or swimming in Upper Broad Creek or Clubfoot Creek. Upper Broad is a great spot. Look out for west winds though. No protection from that way.
I would invite you to Northwest Creek for the day, but the local restaurant closed, so there really isn't anything to come here to do anymore.
A long overnight would be either anchoring in South River or going to River Dunes Marina.
And of course, the brass ring down here is making it to Ocracoke. A wonderful and, dare I say, magical place to visit by boat. Anchor in Silver Lake, grab a cheap spot on the federal docks, or tie up at the Anchorage Marina. There is no wrong way to do it.