Currie Mountain in Douglas, New Brunswick (15 min drive from downtown Fredericton) is the place to go if you're looking for a slightly challenging but not too strenuous 1 hour hike. You'll find it across from Happy Apple Acres (http://happyappleacres.com/), which deserves a visit all on its own. Here is a view of what you'll see on the left side of the road as you park on the shoulder and get ready for your hike... see the St. John River flowing in the background!
We were there in mid-October 2010, a few weeks after a couple different wind and rain storms. This was evidenced very clearly on the mountain as we encountered tree after tree down.
It is a short hike from the bottom to the top and back; it could take you less than hour or more than an hour if you take your time and really meander around the different trails. A nice early evening hike before or after dinner!