There has been a ferry across Halifax Harbour connecting the cities of Halifax and Dartmouth since 1752, shortly after the cities were founded. Currently it is a foot passenger ferry (and bikes) but previous to the first suspension bridge built in the 1950s, the ferry carried cars and, before that, I imagine, horses and carraiges.
The ferry is a nice way to see the Halifax skyline from the water as well. Ferries run all day from about 6 a.m. weekdays until midnight. The cost is $2.00 per trip, less for seniors, students and children. Kids under 5 are free. You can get a paper transfer that will then let you catch a bus from either side as it's all part of the Metro Transit system. That means a paper transfer from a bus will allow you on the ferry, as well.
The ferry ride across the harbour, downtown to downtown, takes about 12 minutes. There is also a ferry connecting the Eastern part of Dartmouth (Woodside) which runs during the morning and afternoon rush hours only. The main downtown ferry runs half hourly in the mornings on weekdays after 9 a.m., evenings on weekdays after 6 p.m. and on weekends, and quarter-hourly in the weekday afternoons and weekday morning rush hour starting at 6:30 a.m. It only runs until midnight (last boat leaves Halifax for Dartmouth at 11:45 p.m. but if there are special events on like the Busker Festival or the Tall Ships then it will run until about 2 a.m.
The Dartmouth side of the ferry lands at a public library and in that building also is a Saturday morning farmer's market, a theatre and there's a park nearby. Also in the area are shops and one or two pubs and restaurants that I would recommend. You can get busses from Alderney drive to MicMac Mall and other shopping areas.