Downtown Halifax is compact and very walkable. The main attractions — the Citadel, the waterfront, the Public Gardens, Spring Garden Road — are all within a comfortable twenty-minute walk of each other. If you are staying on the peninsula, you will not need a car for the central sights.
Halifax Transit runs a reliable bus network across the peninsula and into Dartmouth and the suburbs. Single fares are around CAD 2.75; day passes are available. The downtown terminal on Barrington Street is the main hub. The main limitation is frequency — buses run every 15-30 minutes on most routes, so it is not the system you rely on for flexible daytime touring.
The Halifax ferry to Dartmouth runs every fifteen minutes in peak hours from the Alderney ferry terminal on the Dartmouth side, linking to the Halifax Transit bus network. It is the fastest way to cross the harbour and also a pleasant short trip in its own right. The fare is the same as the bus.
For getting to Africville, the airport, or the outer suburbs, a taxi or Uber is the practical option. Halifax has a good supply of ride-share vehicles. Cycling is possible on the peninsula; there are some dedicated lanes, though the hills and weather can be uninviting for casual riders. Bike rentals are available near the waterfront in summer.