First, welcome to Nova Scotia. I hope you enjoy your visit. The drive to Cape Breton and the Cabot Trail is not a short one, I doubt you'll want to do most of the route over again to visit Sydney. You might want to visit the Bay of Fundy if you're into coastal regions and the world's highest tides. If you time it right a route from Halifax to Truro then Parrsboro to check out the tides. Then off to PEI before nightfall.
If your evenings are free there may be a few sites within an hour or so from Halifax worth seeing. If you are looking for Historical forts and reenactments Louisbourg is having a 300 year party http://louisbourg300.ca/ but that's another long drive to Cape Breton.