Nova Scotia is one of the Maritime provinces of Canada, known as Canada's Ocean's Playground.
Halifax is the capital city of Nova Scotia, Canada. It is also the main city of the Maritimes region. It has a lot of culture for a city of it's size, as it is the largest Canadian city east of Quebec City.
Going North to 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 here, walk straight ahead and 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 is going to the airport, but get a lift there anyway, because it will increase the chances that passing cars are going longer distances. 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. The intersection is quite busy and cars go by fast, so a good option is to get off in the gas station 2-3km before the intersection, where road 2 meets the 102. There's a traffic circle before the on-ramp, so traffic goes slow, and there's plenty of room for cars to stop. 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
If you want to go to the South Shore of Nova Scotia (Mahone Bay, Bridgewater, Lunenburg, etc) from Halifax, take the #52 Bus to Bayers Lake (more walking required) or the #21 to Timberlea (better option). Get off the #21 Bus on Lakelands Blvd across from the car dealership and Tim Horton's, and then walk south toward the only intersection. You'll cross the intersection (carefully!) over to the on-ramp for Highway 103. There is a lot of traffic here heading to the South Shore, especially M-F @ 17:00, so you should have no problem getting a ride if you have a sign.
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.
Border Crossing to Maine, United States
Nova Scotia has no land border crossings with the United States. Nova Star as of 2014 reopened the ferry crossing the border from yarmouth NS, to Portland, Main.  Tickets do cost 100$+ Traveling through to New Brunswick and crossing the border from there is also an option.
Bella and a friend were on the highway from outside Halifax by 20miles and saw a few cops drive by and they didn't bother with them!
There are signs around Halifax stating that no pedestrians are allowed on highway, but out of the city limits there are not any, so, they hitched from outside Halifax to North Sydney to get the boat to Newfoubdland and had a fabulous time. People are friendly and cops seem to not mind.