Thought it rang a bell, I actually met a guy to buy something on that street once...the area didn't strike me as bad or anything, but wasn't terribly quiet either, lots of appartments, (ie a lot of people) around there. From what I recall however, if you plan to take public transit, you've got in all nearby!
Check out this google street view map:
1675,Rue Grenet,St.Laurent, quebec - Google Maps
Turn it around, the shopping cart next to the bus stop made me laugh!!
If you don't mind my asking, where are you moving from, and will you be working in town, or nearby? If you plan to work in town, you may want to get a place a little closer to cote vertu metro station, since that will be a direct shot downtown, and a lot cheaper/faster than driving!