Dan, I presume you want to get to C.B. reasonably quickly and not do a golf tour of the region? If you're in touring mode you could catch the ferry from Sant John, NB to Digby, NS and play the wonderful Stanley Thompson Digby Pines course. A bit further out of the way is my favorite pre-Cabot course in NS, Chester. But I cannot in good conscience advise you to travel to Cabot by way of Chester!
On the way to Cabot from NB is what the scribes would call "a sporty little track", Truro Golf Club, in the town of the same name. Also along the way is Abercrombie Golf Club just outside New Glasgow, which is a fairly brawny course that I always really liked. Partway between Cabot and Highland Links is Cheticamp, which I have not played but one about which I hear good things.
Enjoy your trip. Spectacular weather up here right now, mid-70s, not too humid, not a cloud in the sky.