Fredericton is a very nice city overall, but there are a couple of places you should exercise a bit of caution. Devon, on the north side of town, is a low-income area, and I've known a few people to get mugged while walking there late at night.
Although Fredericton is a very conservative city (because of the government aspect), it is also quite gay-friendly (maybe because of the active arts community). However, gay bashings still occur on occasion, even when the person being bashed isn't even gay.
When the bars get out, drunken rowdies often cruise the streets. Areas like The Green (walkway down by the riverside) are sometimes haunted by people looking for trouble late at night.
Watch out for the blackflies and mosquitos if you come too early - they go crazy in spring and early summer, if you are not in the middle of a city or town. On the other end of the spectrum, be prepared for cold weather and snow if you visit from Nov.- March. This photo of me keeping my driveway clear was taken on a typical February day in the early 1980s (now I have a snowblower)! Lately, global climate change seems to be really messing around with the weather - the last few years giving us a bit of a respite until the winter of 2008 roared back with a vengence (2nd photo)!
One thing I shall never forget about my time in Canada was witnessing my first fatal road traffic accident. It was not on the main highway, but on the graded dirt road leading to our camp at Lauvina. A colleague and I were returning to camp at dusk when we saw headlights coming towards us but some distance away. Suddenly the lights disappeared and we heard a dull thud. We ran along the track and came across an upturned Canadian military 'Jeep' (can't remember the exact make). The two occupants had been drinking and on driving along the road had misjudged a curve, at speed, and the vehicle flipped over. We found one occupant badly injured at the side of the road, and the other was beyond help. I was 19 at that time, but it is an accident that has stayed with me all of my life. And it was all down to too much alcohol!
If travelling here during the months of November through March---bring something warm!! Temps can dip down to -25 without the windchill...