Start by taking the ferry across the harbour. It's like being "Screeched In" in Newfoundland, really. Well, you'll be less hammered at the end of the experience, but you'll feel like a local. Depending on the time of year, you could be enveloped in a pea-soup fog or get the best harbour view to be found, still only $2.25 a trip.
Two ferries to choose from: one will take you to Woodside, near the Nova Scotia Community College campus and the city's best Value Village (375 Pleasant Street). Also in Woodside is John's Lunch (352 Pleasant Street), one of the best fish and chip joints in town. From there you can take the 60 bus to Eastern Passage, just past the refinery, where you can have lunch at cool diner Emma's Eatery (31 Cow Bay Road), or catch a ferry to McNabs Island (mcnabsisland.com), a great place for a hike.
The other ferry takes you to downtown Dartmouth at Alderney Landing. The pub food at Celtic Corner (69 Alderney Drive) is solid, and a stroll up Portland Street for the shops and local colour is recommended. A block over, Two If By Sea (66 Ochterloney Street) has the biggest, most buttery croissants in the city. For a dressier time later in the day, try Nectar Social House (62 Ochterloney Street) for a cocktail or multi-course meal, or La Perla (73 Alderney Drive) for Italian.
From there, walk up King Street to the Dartmouth Common, north to Wyse Road and past the Dartmouth Sportsplex and the Metro Transit Bridge Terminal. Turn left there and onto the pedestrian walkway of the Macdonald Bridge. The view over Halifax is unparalleled (you can see the Navy shipyards) and but if you have a fear of heights, you might want to catch a bus across instead.
Once back in Halifax, you're in the north end, between the bridges, as Sloan once described it. Walk along North Street and hit Java Blend (6027 North Street) for coffee or FRED. beauty food art (2606 Agricola Street) for one of the best cupcakes you'll ever eat (aside from a cafe, it's also an art gallery and a hair salon). If you're at that corner in the evening, across the way is Gus' Pub & Grill (2605 Agricola Street), ground zero for the city's rock scene.
From here you can choose to walk south on Agricola a couple of blocks where you'll find the Roberts Street Social Centre (5684 Roberts Street, robertsstreet.org), home of the Anchor Archive Zine Library and artists in residence through the summer, and a whole bunch more. Keep their limited hours in mind, though: Tuesday 6-8pm and Sunday 2-5pm. Or keep walking south on Agricola and on the right side you'll see Obsolete Records (2454 Agricola Street) for the best in local music.
If you choose to head north up Agricola from Fred, check out antiques row, places such as Finer Things, (2797 Agricola Street) Belissimo! (2743 Agricola Street) and Almanac Antiques, Books & Records (2820 Isleville Street).
A 10-minute walk north and you'll find yourself in the Hydrostone, a suburb of unique houses constructed following the Halifax Explosion. At Young and Isleville Streets there's a tony row of boutiques and eateries, offering everything from folk art to baked goods to sushi in the Hydrostone Market (hydrostonemarket.ca). And just a little further up the hill is the lovely Fort Needham park, the best spot to see where the Halifax Explosion took place in 1917.