Beaufort is more a marina town than a beach town. Are you into boating? Look at Google Maps satellite image for an idea of how boating-focused it is.
You mention exploring up and down the coast, but going north from Beaufort is not especially convenient. If you wanted to go to Roanoke Island, for example, you would be better off staying in Manteo or Nag’s Head.
Can’t speak to rental availability, but Easter is well ahead of the peak season (water too cold for swimming) so I expect you can find something.
How far afield do you want to explore? Beaufort has plenty of touristy things to do, and Carrot Island is very nearby and is absolutely glorious. The week we spent in Beaufort, we ate ourselves silly on delicious seafood and canoed over to Carrot Island every day to pad around and watch the herds of wild horses; we didn’t do that much driving.
If you want to see a lot of different places, maybe consider Wilmington or Wrightsville Beach or something in that area? Much more developed, but it’s within an hour’s drive of a lot of good stuff.
I have some personal history there. My ex-wife and I were married at the chapel on the grounds of Christ Episcopal Church there, and her father had grown up there. He kept a boat in the marina there for a long time, so we went back from time to time to enjoy the Neuse River.
Aside from all of that, though, I remember it as a charming little town content to be a charming little town. Which is nice.
Also, being a native South Carolinian, I don’t find much about North Carolina beaches to get excited about. The Outer Banks were impressive when I went there ca. 1981, but the last time I went out there, it was even more overdeveloped than South Carolina’s beaches are.
Remember you can use Google Street View and get a virtual tour of an area before you visit. All those little communities like Nags Head, Kitty Hawk, and Duck are pretty nice. I am not positive but I wouldn’t think it would be terribly crowded at Easter because it’s not really warm enough to swim yet.
It’s Memorial Day weekend that the Outer Banks starts getting heinously busy. Before that and after Labor Day are pretty nice.
Nag’s Head, Duck, etc. are, as KneadToKnow said, quite overdeveloped, which is really too bad, IMO, but on the other hand, it might be fine for you depending on what you want to do. As has already been said, it’ll be too cold for swimming, so I assume you’ve got other activities in mind.
A lot of our seafood here comes from the Core Sound, with the fishermen living on Harker’s Island, so you will find some good eats out that way. Clams, bluefish, and sea bass should be in season then.
I went to Wilmington in the middle of September two years ago and it was really nice. Not too crowded and still warm enough to be out on the water and such.