Probably your best bet is to chase Striped Bass. The numbers have exploded in the last decade, making this fishery world class.
A few years ago we surf fished Miscou Island...wet waded the beautiful sand beaches by day, feasted on lobster, clams, mussels and oysters at night. Great getaway. Heavy bass or pike gear is all you need. If you're going to specifically surf fish then a 9 ft + rod is helpful. Stripers really put up battle and are great on the grill too.
Not sure what the best spots are that time of year...they generally migrate up the rivers (the Miramichi gets a huge run) in late spring and by late summer you can fish the surf.
https://www.outdoorcanada.ca/13-new-brunswick-hot-spots-for-striped-bass-fishing/