Moncton is a city in Southeastern New Brunswick. It has a great library, is a major hub for freight trains, and has a busy main strip where people play music. There's a mellow attitude in the city and plenty of places to get alcohol, plus a decent tobbaconist.
Getting out of Moncton shouldn't be too difficult. If you pass through, it's worth recording how you got out.
West to Fredericton
Mountain Road (126) leads west out of Moncton to the TCH junction. The usual suspects are there: McDonalds, Subway, Tim Hortons, an Esso gas station. Hitch on the TCH itself if the on-ramp seems a little quiet.
Drumroots got lucky and the lift that bought him to Moncton from Truro took a detour to drop him back on the TCH to continue hitching.
South-West to Saint John
South-East to to Nova Scotia
East to Prince Edward Island
There are two ways to go to PEI, one on the road 15 or 16. One of the easiest way to go out of the city in the direction of both roads is to go the traffic light where the road 15 crosses the road 134  with a sign. When you get dropped at the bridge there is a free shuttle (free only going on the island, $4.50 the other way) crossing the bridge.
North to Miramichi
Nomadwiki & Trashwiki
Check Nomadwiki for info on accommodation, showers etc. or Trashwiki for dumpsters...and share your wisdom :)