Yeah, Griffintown is on the comeup. It's getting nicer & nicer. Plus you're right next to downtown, close to the highway, close to a subway, close to Atwater market, not too far from a Costco. It's a pretty nice place to live.
I've lived here my whole life, but Notre-Dame de Grace has a lot of nice places to rent and it's a pretty calm, residential neighborhood (as long as you stay north of Sherbrooke). The only downside (and I guess it's a big one if you go out a lot) is that there's not much in terms of night life. You have the Monkland village (and even then, you're pretty limited), but really outside of that it's not a very lively part of town like Mile End.
West Island is much more anglophone if you prefer that, although I don't know the area all that much.