Moncton's downtown is easily reconnoitered on foot -- if you can find parking. (Look for lots a block just north and south of Main St.) Downtown Moncton, Inc., publishes a nicely designed "Historic Walking Tour" brochure that touches upon some of the most significant buildings; ask for it at the visitor center.
The most active stretch of Main Street is the section between City Hall and the train underpass: an accumulation of cafes, newsstands, hotels, and restaurants, plus a handful of shops. There's also quite a mix of architectural styles here, the earliest examples of which testify to Moncton's former prosperity and prominence as a regional center of commerce.
Exploring by bike is a good idea, especially if you go pedaling along Riverfront Park or through the 121 hectares (300 acres) of popular Centennial Park. The local bike club Hub City Wheelers sometimes schedules group bike rides, which nonmembers are welcome to join; it's a good way to meet local cyclists and find the most scenic routes. Ask about the rides at the visitor center.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.