For whatever reason, New Brunswick isn't usually considered a top priority when first-time travelers begin hatching plans to visit the eastern provinces. Even within Canada, the province is as well known for its pulp mills, industrial forests, cargo ports, and refineries (Irving Oil is based here) as for its cute villages, high tides, fresh air, or friendly locals.
And to foreigners? The place is mostly confused with the same-named city in New Jersey. Either that, or it's viewed as a place to be driven through as quickly as possible en route to Nova Scotia and Prince Edward Island.
Rest assured, though: New Brunswick does have pockets of wilderness and scenic beauty that equal those anywhere in eastern Canada, and plenty of great cultural offerings. (FDR was crazy about the place.) This province's appeals are just a bit less obvious than those of, say, Cape Breton.
So you'll need to do a little homework before heading there, but if you do, you can definitely cobble together a number of fun excursions taking in the province's variegated landscapes. You can lounge in surprisingly warm ocean waters lapping up on sandy beaches that hold their own to anything Prince Edward Island's got to offer. You can shutterbug it on rocky, surf-pounded headlands that look like the far shores of Newfoundland. You can gape at huge tides that will stun the kids with their drop and power. You can even browse through a chocolate museum (which must be the best idea for a museum by anyone, anywhere, ever).
You could also make time to explore a salty, pubby maritime city, Saint John, that makes a nice run at copying Halifax's mix of arts, culture, beer, and a busy working harbor.
Some weather-numbers watchers claim this province has the warmest summers and sunniest winters in the country, on average -- and the provincial tourism commission has been all too eager to jump on these stats as proof that there's something magical here. But I think that's missing the point. I don't think they need to reach so far.
My advice is just this: Go explore New Brunswick beyond the highways, beyond the first glance. Do that, and you'll find it to be a place full of lovely landscapes, friendly locals, and fun things to do.