Halifax is the capital city of Nova Scotia, Canada, as well as the largest city in that province and indeed the larger Maritimes region. Halifax proper mainly consists of the old city, located on the Halifax peninsula, as well as nearby western suburbs like Spryfield and Clayton Park just across the isthmus. The Halifax Regional Municipality, however, includes communities like Dartmouth across the harbour, Bedford and Sackville to the north, and many rural communities that are further out and not even served by public transit.
You will probably need to take the bus to get anywhere useful for hitchhiking. As of November 5, 2019, bus fare is $2.75 on most buses, and $4.25 for express buses (such as the bus to the airport). The Halifax Transit website is worth consulting for any changes.
Going North to Truro, Cape Breton, New Brunswick, Quebec, and the rest of Canada
Take the #55 Port Wallace bus from the Bridge Terminal in Dartmouth , and get off at the last stop, where it turns around. From there, walk straight ahead to your right and climb up the hill to Highway 118. You want to be on the side closest to the bus stop. There is a good wide place to pull over here and good visibility. A lot of the traffic will be going to the airport, but you can get a lift there anyway, since it's a decent place to hitchhike further.
Take #320 Airport/Fall River either from the Bridge Terminal in Dartmouth or from Scotia Square downtown - one of which should be walkable, for most people, from most parts of peninsular Halifax. The #320 is an express bus that goes all the way to the airport. It costs $1.50 extra ($4.25), so you probably don't want to have to take another bus to catch it.
If you are going to Cape Breton, you need to get off near Truro (the next big town, about an hour drive). Tell your driver and they should know where to drop you off, where the 102 meets the 104. Good luck!
Going North West
Highway 101 goes to Wolfville, Kentville, the rest of The Valley, and Yarmouth. Take the #80 Sackville bus to the Sackville Terminal and then climb up on the highway on ramp to get a lift. A lot of people commute from the Valley into town for work, and Wolfville is a big university town, so this road is quite well traveled.
Going South West
You want to get onto highway 103 to get to Mahone Bay, Bridgewater, and other South shore towns, so take the #52 Bayers Lake or the #21 Timberlea bus to Lakelands Blvd, and then walk south out to the highway. There is a big sign here for the vehicle traffic, so you should have no problem getting in the right spot.
If you're heading to Cape Breton from Halifax, going by the Eastern Shore is a good alternative to the highway. It will be slower, but more scenic and there's many nice places to stop on the way. To get out of Halifax, take any bus to Bridge Terminal, and then #401(doesn't run on weekends), #61 or #68 to Cherrybrook and ask to be let off on road 7/107 the farthest away from town (the buses might cross that road a few times on the way). From there just walk heading east and pick whatever spot looks good enough. You can take road 7 all the way to Antigonish, where it meets the main highway to Cape Breton.
Lake Major Road is the last traffic light near where the bus drops you off, any further up the cars are going too fast. If you wait on the other (east) side of the lights there's a turning lane that cars can pull in to.